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Precalculus Enhanced with Graphing Utilities 7th Edition Sullivan Test Bank

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Precalculus Enhanced with Graphing Utilities 7th Edition Sullivan Test Bank

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Product Details:

  • ISBN-10 ‏ : ‎ 0134119282
  • ISBN-13 ‏ : ‎ 978-0134119281
  • Author:  Michael Sullivan

Prepare, Practice, Review The Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The Enhanced with Graphing Utilities Series has evolved to meet today’s course needs by integrating the usage of graphing calculators, active-learning, and technology in new ways to help students be successful in their course, as well as in their future endeavors. In the Seventh Edition, there are several new features that appear in both the text and MyMathLab. Retain Your Knowledge problems offer the type of “final exam material” that students can use to maintain their skills throughout each chapter.

 

Table of Content:

  1. 1 Graphs
  2. Outline
  3. 1.1The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations
  4. PREPARING FOR THIS SECTION
  5. Objectives
  6. Rectangular Coordinates
  7. Graphing Utilities
  8. Use the Distance Formula
  9. Example 1 Finding the Distance between Two Points
  10. Solution
  11. Proof of the Distance Formula
  12. Example 2 Finding the Length of a Line Segment
  13. Solution
  14. Example 3 Using Algebra to Solve Geometry Problems
  15. Solution
  16. Use the Midpoint Formula
  17. Example 4 Finding the Midpoint of a Line Segment
  18. Solution
  19. Graph Equations by Plotting Points
  20. Example 5 Determining Whether a Point Is on the Graph of an Equation
  21. Solution
  22. Example 6 Graphing an Equation by Plotting Points
  23. Step-by-Step Solution
  24. Example 7 Graphing an Equation by Plotting Points
  25. Solution
  26. Graph Equations Using a Graphing Utility
  27. Example 8 Expressing an Equation in the Form y = {expression in x}
  28. Solution
  29. Example 9 Graphing an Equation Using a Graphing Utility
  30. Step-by-Step Solution
  31. Use a Graphing Utility to Create Tables
  32. Example 10 Creating a Table Using a Graphing Utility
  33. Step-by-Step Solution
  34. Find Intercepts from a Graph
  35. Example 11 Finding Intercepts from a Graph
  36. Solution
  37. Use a Graphing Utility to Approximate Intercepts
  38. Example 12 Approximating Intercepts Using a Graphing Utility
  39. Solution
  40. 1.1 Assess Your Understanding
  41. Concepts and Vocabulary
  42. Skill Building
  43. Applications and Extensions
  44. Explaining Concepts: Discussion and Writing
  45. ‘Are You Prepared?’ Answers
  46. 1.2 Intercepts; Symmetry; Graphing Key Equations
  47. PREPARING FOR THIS SECTION
  48. Objectives
  49. Find Intercepts Algebraically from an Equation
  50. Example 1 Finding Intercepts from an Equation
  51. Solution
  52. Test an Equation for Symmetry
  53. Example 2 Symmetric Points
  54. Example 3 Finding Intercepts and Testing an Equation for Symmetry
  55. Solution
  56. Seeing the Concept
  57. Know How to Graph Key Equations
  58. Example 4 Graphing the Equation y = x3 by Finding Intercepts and Checking for Symmetry
  59. Solution
  60. Example 5 Graphing the Equation x = y2
  61. Solution
  62. Example 6 Graphing the Equation y=1x
  63. Solution
  64. 1.2 Assess Your Understanding
  65. Concepts and Vocabulary
  66. Skill Building
  67. Mixed Practice
  68. Applications and Extensions
  69. Explaining Concepts: Discussion and Writing
  70. 1.3 Solving Equations Using a Graphing Utility
  71. PREPARING FOR THIS SECTION
  72. Objective
  73. Solve Equations Using a Graphing Utility
  74. Example 1 Using ZERO (or ROOT) to Approximate Solutions of an Equation
  75. Solution
  76. Example 2 Using INTERSECT to Approximate Solutions of an Equation
  77. Solution
  78. 1.3 Assess Your Understanding
  79. Concepts and Vocabulary
  80. Skill Building
  81. 1.4 Lines
  82. Objectives
  83. Calculate and Interpret the Slope of a Line
  84. Example 1 Finding and Interpreting the Slope of a Line Given Two Points
  85. Square Screens
  86. Exploration
  87. Exploration
  88. Graph Lines Given a Point and the Slope
  89. Example 2 Graphing a Line Given a Point and a Slope
  90. Solution
  91. Find the Equation of a Vertical Line
  92. Example 3 Graphing a Line
  93. Solution
  94. Use the Point–Slope Form of a Line; Identify Horizontal Lines
  95. Example 4 Using the Point–Slope Form of a Line
  96. Example 5 Finding the Equation of a Horizontal Line
  97. Solution
  98. Write the Equation of a Line in Slope–Intercept Form
  99. Seeing the Concept
  100. Seeing the Concept
  101. Example 6 Finding the Slope and y-Intercept
  102. Solution
  103. Find the Equation of a Line Given Two Points
  104. Example 7 Finding an Equation of a Line Given Two Points
  105. Solution
  106. Graph Lines Written in General Form Using Intercepts
  107. Example 8 Graphing an Equation in General Form Using Its Intercepts
  108. Solution
  109. Find Equations of Parallel Lines
  110. Example 9 Showing That Two Lines Are Parallel
  111. Solution
  112. Example 10 Finding a Line That Is Parallel to a Given Line
  113. Solution
  114. Find Equations of Perpendicular Lines
  115. Proof
  116. Example 11 Finding the Slope of a Line Perpendicular to Another Line
  117. Example 12 Finding the Equation of a Line Perpendicular to a Given Line
  118. Solution
  119. 1.4 Assess Your Understanding
  120. Concepts and Vocabulary
  121. Skill Building
  122. Applications and Extensions
  123. Explaining Concepts: Discussion and Writing
  124. 1.5 Circles
  125. PREPARING FOR THIS SECTION
  126. OBJECTIVES
  127. Write the Standard Form of the Equation of a Circle
  128. Example 1 Writing the Standard Form of the Equation of a Circle
  129. Solution
  130. Graph a Circle by Hand and by Using a Graphing Utility
  131. Example 2 Graphing a Circle by Hand and by Using a Graphing Utility
  132. Solution
  133. Example 3 Finding the Intercepts of a Circle
  134. Solution
  135. Work with the General Form of the Equation of a Circle
  136. Example 4 Graphing a Circle Whose Equation Is in General Form
  137. Solution
  138. Example 5 Finding the General Equation of a Circle
  139. Solution
  140. Overview
  141. 1.5 Assess Your Understanding
  142. Concepts and Vocabulary
  143. Skill Building
  144. Applications and Extensions
  145. Explaining Concepts: Discussion and Writing
  146. Chapter Review
  147. Things to Know
  148. Objectives
  149. Review Exercises
  150. Chapter Test
  151. Chapter Projects
  152. 2 Functions and Their Graphs
  153. Outline
  154. A Look Back
  155. A Look Ahead
  156. 2.1 Functions
  157. Preparing for this Section
  158. OBJECTIVES
  159. Determine Whether a Relation Represents a Function
  160. Example 1 Maps and Ordered Pairs as Relations
  161. EXAMPLE 2 Determining Whether a Relation Is a Function
  162. Solution
  163. EXAMPLE 3 Determining Whether a Relation Is a Function
  164. Solution
  165. EXAMPLE 4 Determining Whether an Equation Is a Function
  166. Solution
  167. EXAMPLE 5 Determining Whether an Equation Is a Function
  168. Solution
  169. Find the Value of a Function
  170. EXAMPLE 6 Finding Values of a Function
  171. Solution
  172. EXAMPLE 7 Finding Values of a Function on a Calculator
  173. Comment
  174. Implicit Form of a Function
  175. Find the Difference Quotient of a Function
  176. EXAMPLE 8 Finding the Difference Quotient of a Function
  177. Solution
  178. Find the Domain of a Function Defined by an Equation
  179. EXAMPLE 9 Finding the Domain of a Function
  180. Solution
  181. EXAMPLE 10 Finding the Domain in an Application
  182. Solution
  183. Form the Sum, Difference, Product, and Quotient of Two Functions
  184. EXAMPLE 11 Operations on Functions
  185. Solution
  186. 2.1 Assess Your Understanding
  187. Concepts and Vocabulary
  188. Skill Building
  189. Applications and Extensions
  190. Explaining Concepts: Discussion and Writing
  191. 2.2 The Graph of a Function
  192. Preparing for this Section
  193. OBJECTIVES
  194. Identify the Graph of a Function
  195. EXAMPLE 1 Identifying the Graph of a Function
  196. Solution
  197. Obtain Information from or about the Graph of a Function
  198. EXAMPLE 2 Obtaining Information from the Graph of a Function
  199. Solution
  200. EXAMPLE 3 Obtaining Information about the Graph of a Function
  201. Solution
  202. EXAMPLE 4 Average Cost Function
  203. Solution
  204. 2.2 Assess Your Understanding
  205. Concepts and Vocabulary
  206. Skill Building
  207. Applications and Extensions
  208. Explaining Concepts: Discussion and Writing
  209. 2.3 Properties of Functions
  210. Preparing for This Section
  211. Objectives
  212. Determine Even and Odd Functions from a Graph
  213. EXAMPLE 1 Determining Even and Odd Functions from the Graph
  214. Solution
  215. Identify Even and Odd Functions from an Equation
  216. EXAMPLE 2 Identifying Even and Odd Functions
  217. Solution
  218. Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant
  219. EXAMPLE 3 Determining Where a Function Is Increasing, Decreasing, or Constant from Its Graph
  220. Solution
  221. Use a Graph to Locate Local Maxima and Local Minima
  222. EXAMPLE 4 Finding Local Maxima and Local Minima from the Graph of a Function and Determining Where the Function Is Increasing, Decreasing, or Constant
  223. Solution
  224. Use a Graph to Locate the Absolute Maximum and the Absolute Minimum
  225. EXAMPLE 5 Finding the Absolute Maximum and the Absolute Minimum from the Graph of a Function
  226. Solution
  227. Use a Graphing Utility to Approximate Local Maxima and Local Minima and to Determine Where a Function Is Increasing or Decreasing
  228. EXAMPLE 6 Using a Graphing Utility to Approximate Local Maxima and Minima and to Determine Where a Function Is Increasing or Decreasing
  229. Solution
  230. Find the Average Rate of Change of a Function
  231. EXAMPLE 7 Finding the Average Rate of Change
  232. Solution
  233. The Secant Line
  234. EXAMPLE 8 Finding the Equation of a Secant Line
  235. Solution
  236. 2.3 Assess Your Understanding
  237. Concepts and Vocabulary
  238. Skill Building
  239. Applications and Extensions
  240. Explaining Concepts: Discussion and Writing
  241. 2.4 Library of Functions; Piecewise-defined Functions
  242. Preparing for This Section
  243. Objectives
  244. Graph the Functions Listed in the Library of Functions
  245. EXAMPLE 1 Graphing the Cube Root Function
  246. Solution
  247. EXAMPLE 2 Graphing the Absolute Value Function
  248. Solution
  249. Seeing the Concept
  250. Comment
  251. Graph Piecewise-defined Functions
  252. EXAMPLE 3 Graphing a Piecewise-defined Function
  253. Solution
  254. EXAMPLE 4 Analyzing a Piecewise-defined Function
  255. Solution
  256. EXAMPLE 5 Cost of Electricity
  257. Solution
  258. 2.4 Assess Your Understanding
  259. Concepts and Vocabulary
  260. Skill Building
  261. Applications and Extensions
  262. Explaining Concepts: Discussion and Writing
  263. 2.5 Graphing Techniques: Transformations
  264. Objectives
  265. Graph Functions Using Vertical and Horizontal Shifts
  266. Exploration
  267. Result
  268. Example 1 Vertical Shift Down
  269. Solution
  270. Exploration
  271. Result
  272. Example 2 Combining Vertical and Horizontal Shifts
  273. Solution
  274. Graph Functions Using Compressions and Stretches
  275. Exploration
  276. Result
  277. Exploration
  278. Result
  279. Example 3 Graphing Using Stretches and Compressions
  280. Solution
  281. Graph Functions Using Reflections about the x-Axis or y-Axis
  282. Exploration
  283. Result
  284. Exploration
  285. Result
  286. Example 4 Determining the Function Obtained from a Series of Transformations
  287. Solution
  288. Example 5 Combining Graphing Procedures
  289. Solution
  290. Example 6 Combining Graphing Procedures
  291. Solution
  292. 2.5 Assess Your Understanding
  293. Concepts and Vocabulary
  294. Skill Building
  295. Applications and Extensions
  296. Explaining Concepts: Discussion and Writing
  297. 2.6 Mathematical Models: Building Functions
  298. Objective
  299. Build and Analyze Functions
  300. Example 1 Finding the Distance from the Origin to a Point on a Graph
  301. Solution
  302. Example 2 Area of a Rectangle
  303. Solution
  304. Example 3 Close Call?
  305. Solution
  306. 2.6 Assess Your Understanding
  307. Applications and Extensions
  308. Chapter Review
  309. Library of Functions
  310. Things to Know
  311. Objectives
  312. Review Exercises
  313. Chapter Test
  314. Cumulative Review
  315. Chapter Projects
  316. 3 Linear and Quadratic Functions
  317. Outline
  318. A Look Back
  319. A Look Ahead
  320. 3.1 Properties of Linear Functions and Linear Models
  321. Preparing for This Section
  322. Objectives
  323. 1 Graph Linear Functions
  324. Example 1 Graphing a Linear Function
  325. Solution
  326. 2 Use Average Rate of Change to Identify Linear Functions
  327. Proof
  328. Example 2 Using the Average Rate of Change to Identify Linear Functions
  329. Solution
  330. 3 Determine Whether a Linear Function Is Increasing, Decreasing, or Constant
  331. Example 3 Determining Whether a Linear Function Is Increasing, Decreasing, or Constant
  332. Solution
  333. 4 Build Linear Models from Verbal Descriptions
  334. Example 4 Straight-line Depreciation
  335. Solution
  336. Example 5 Supply and Demand
  337. Solution
  338. 3.1 Assess Your Understanding
  339. Concepts and Vocabulary
  340. Skill Building
  341. Applications and Extensions
  342. Mixed Practice
  343. Explaining Concepts: Discussion and Writing
  344. Retain Your Knowledge
  345. 3.2 Building Linear Models from Data
  346. Preparing for This Section
  347. Objectives
  348. 1 Draw and Interpret Scatter Diagrams
  349. Example 1 Drawing and Interpreting a Scatter Diagram
  350. Solution
  351. 2 Distinguish between Linear and Nonlinear Relations
  352. Example 2 Distinguishing between Linear and Nonlinear Relations
  353. Solution
  354. Example 3 Finding a Model for Linearly Related Data
  355. Solution
  356. 3 Use a Graphing Utility to Find the Line of Best Fit
  357. Example 4 Finding a Model for Linearly Related Data
  358. Solution
  359. 3.2 Assess Your Understanding
  360. Concepts and Vocabulary
  361. Skill Building
  362. Applications and Extensions
  363. Mixed Practice
  364. Explaining Concepts: Discussion and Writing
  365. Retain Your Knowledge
  366. 3.3 Quadratic Functions and Their Properties
  367. Preparing for This Section
  368. Objectives
  369. Quadratic Functions
  370. 1 Graph a Quadratic Function Using Transformations
  371. Example 1 Graphing a Quadratic Function Using Transformations
  372. Solution
  373. 2 Identify the Vertex and Axis of Symmetry of a Quadratic Function
  374. Example 2 Locating the Vertex without Graphing
  375. Solution
  376. 3 Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts
  377. Example 3 How to Graph a Quadratic Function by Hand Using Its Properties
  378. Step-by-Step Solution
  379. Example 4 Graphing a Quadratic Function Using Its Vertex, Axis, and Intercepts
  380. Solution
  381. Example 5 Graphing a Quadratic Function Using Its Vertex, Axis, and Intercepts
  382. Solution
  383. 4 Find a Quadratic Function Given Its Vertex and One Other Point
  384. Example 6 Finding the Quadratic Function Given Its Vertex and One Other Point
  385. Solution
  386. 5 Find the Maximum or Minimum Value of a Quadratic Function
  387. Example 7 Finding the Maximum or Minimum Value of a Quadratic Function
  388. Solution
  389. 3.3 Assess Your Understanding
  390. Concepts and Vocabulary
  391. Skill Building
  392. Mixed Practice
  393. Applications and Extensions
  394. Explaining Concepts: Discussion and Writing
  395. Retain Your Knowledge
  396. 3.4 Build Quadratic Models from Verbal Descriptions and from Data
  397. Preparing For This Section
  398. Objectives
  399. 1 Build Quadratic Models from Verbal Descriptions
  400. Example 1 Maximizing Revenue
  401. Solution
  402. Example 2 Maximizing the Area Enclosed by a Fence
  403. Solution
  404. Example 3 Analyzing the Motion of a Projectile
  405. Solution
  406. Example 4 The Golden Gate Bridge
  407. Solution
  408. 2 Build Quadratic Models from Data
  409. Example 5 Fitting a Quadratic Function to Data
  410. Solution
  411. 3.4 Assess Your Understanding
  412. Applications and Extensions
  413. Mixed Practice
  414. Explaining Concepts: Discussion and Writing
  415. Retain Your Knowledge
  416. 3.5 Inequalities Involving Quadratic Functions
  417. Preparing For This Section
  418. Objective
  419. 1 Solve Inequalities Involving a Quadratic Function
  420. Example 1 Solving an Inequality
  421. By Hand Solution
  422. Graphing Utility Solution
  423. Example 2 Solving an Inequality
  424. Solution
  425. Example 3 Solving an Inequality
  426. Solution
  427. 3.5 Assess Your Understanding
  428. Skill Building
  429. Mixed Practice
  430. Applications and Extensions
  431. Explaining Concepts: Discussion and Writing
  432. Retain Your Knowledge
  433. Chapter Review
  434. Things to Know
  435. Objectives
  436. Review Exercises
  437. Chapter Test
  438. Cumulative Review
  439. Chapter Projects
  440. 4 Polynomial and Rational Functions
  441. Outline
  442. A Look Back
  443. A Look Ahead
  444. 4.1 Polynomial Functions and Models
  445. PREPARING FOR THIS SECTION
  446. Objectives
  447. Identify Polynomial Functions and Their Degree
  448. Example 1 Identifying Polynomial Functions
  449. Solution
  450. Power Functions
  451. Exploration
  452. Exploration
  453. Graph Polynomial Functions Using Transformations
  454. Example 2 Graphing a Polynomial Function Using Transformations
  455. Solution
  456. Example 3 Graphing a Polynomial Function Using Transformations
  457. Solution
  458. Identify the Real Zeros of a Polynomial Function and Their Multiplicity
  459. Example 4 Finding a Polynomial Function from Its Zeros
  460. Solution
  461. Seeing the Concept
  462. Example 5 Identifying Zeros and Their Multiplicities
  463. Example 6 Investigating the Role of Multiplicity
  464. Solution
  465. Turning Points
  466. Exploration
  467. Example 7 Identifying the Graph of a Polynomial Function
  468. Solution
  469. End Behavior
  470. Example 8 Identifying the Graph of a Polynomial Function
  471. Solution
  472. Example 9 Writing a Polynomial Function from Its Graph
  473. Solution
  474. Analyze the Graph of a Polynomial Function
  475. Example 10 How to Analyze the Graph of a Polynomial Function
  476. Step-by-Step Solution
  477. Example 11 How to Use a Graphing Utility to Analyze the Graph of a Polynomial Function
  478. Step-by-Step Solution
  479. Build Cubic Models from Data
  480. Example 12 A Cubic Function of Best Fit
  481. Solution
  482. 4.1 Assess Your Understanding
  483. Concepts and Vocabulary
  484. Skill Building
  485. Applications and Extensions
  486. Explaining Concepts: Discussion and Writing
  487. 4.2 The Real Zeros of a Polynomial Function
  488. PREPARING FOR THIS SECTION
  489. Objectives
  490. Use the Remainder and Factor Theorems
  491. Example 1 Using the Remainder Theorem
  492. Solution
  493. Comment
  494. Proof
  495. Example 2 Using the Factor Theorem
  496. Solution
  497. Proof
  498. Use Descartes’ Rule of Signs to Determine the Number of Positive and the Number of Negative Real Zeros of a Polynomial Function
  499. Example 3 Using the Number of Real Zeros Theorem and Descartes’ Rule of Signs
  500. Solution
  501. Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polynomial Function
  502. Example 4 Listing Potential Rational Zeros
  503. Solution
  504. Find the Real Zeros of a Polynomial Function
  505. Example 5 How to Find the Real Zeros of a Polynomial Function
  506. Step-by-Step Solution
  507. Example 6 Finding the Real Zeros of a Polynomial Function
  508. Solution
  509. Solve Polynomial Equations
  510. Example 7 Solving a Polynomial Equation
  511. Solution
  512. Use the Theorem for Bounds on Zeros
  513. Proof (Outline)
  514. Example 8 Finding Upper and Lower Bounds of Zeros
  515. Solution
  516. Example 9 Obtaining Graphs Using Bounds on Zeros
  517. Solution
  518. Example 10 Finding the Real Zeros of a Polynomial Function
  519. Solution
  520. Use the Intermediate Value Theorem
  521. Example 11 Using the Intermediate Value Theorem and a Graphing Utility to Locate Zeros
  522. Solution
  523. 4.2 Assess Your Understanding
  524. Concepts and Vocabulary
  525. Skill Building
  526. Applications and Extensions
  527. Discussion and Writing
  528. 4.3 Complex Zeros; Fundamental Theorem of Algebra
  529. PREPARING FOR THIS SECTION
  530. Objectives
  531. Proof
  532. Use the Conjugate Pairs Theorem
  533. Proof
  534. Proof
  535. Example 1 Using the Conjugate Pairs Theorem
  536. Solution
  537. Find a Polynomial Function with Specified Zeros
  538. Example 2 Finding a Polynomial Function Whose Zeros Are Given
  539. Solution
  540. Proof
  541. Find the Complex Zeros of a Polynomial Function
  542. Example 3 Finding the Complex Zeros of a Polynomial Function
  543. Solution
  544. 4.3 Assess Your Understanding
  545. Concepts and Vocabulary
  546. Skill Building
  547. Discussion and Writing
  548. 4.4 Properties of Rational Functions
  549. Preparing for This Section
  550. Objectives
  551. Find the Domain of a Rational Function
  552. Example 1 Finding the Domain of a Rational Function
  553. Example 2 Graphing y=1×2
  554. Solution
  555. Example 3 Using Transformations to Graph a Rational Function
  556. Solution
  557. Asymptotes
  558. Exploration
  559. Result
  560. Find the Vertical Asymptotes of a Rational Function
  561. Example 4 Finding Vertical Asymptotes
  562. Solution
  563. Exploration
  564. Result
  565. Find the Horizontal or Oblique Asymptote of a Rational Function
  566. Example 5 Finding a Horizontal Asymptote
  567. Solution
  568. Example 6 Finding a Horizontal or Oblique Asymptote
  569. Solution
  570. Example 7 Finding a Horizontal or Oblique Asymptote
  571. Solution
  572. Example 8 Finding a Horizontal or Oblique Asymptote
  573. Solution
  574. 4.4 Assess Your Understanding
  575. Concepts and Vocabulary
  576. Skill Building
  577. Applications and Extensions
  578. Explaining Concepts: Discussion and Writing
  579. 4.5 The Graph of a Rational Function
  580. Preparing for This Section
  581. Objectives
  582. Analyze the Graph of a Rational Function
  583. Example 1 How to Analyze the Graph of a Rational Function
  584. Example 2 Analyzing the Graph of a Rational Function
  585. Solution
  586. Example 3 Analyzing the Graph of a Rational Function
  587. Solution
  588. Example 4 Analyzing the Graph of a Rational Function
  589. Solution
  590. Example 5 Analyzing the Graph of a Rational Function with a Hole
  591. Solution
  592. Example 6 Constructing a Rational Function from Its Graph
  593. Solution
  594. Solve Applied Problems Involving Rational Functions
  595. Example 7 Finding the Least Cost of a Can
  596. Solution
  597. 4.5 Assess Your Understanding
  598. Concepts and Vocabulary
  599. Skill Building
  600. Applications and Extensions
  601. Explaining Concepts: Discussion and Writing
  602. 4.6 Polynomial and Rational Inequalities
  603. Preparing for This Section
  604. Objectives
  605. Solve Polynomial Inequalities Algebraically and Graphically
  606. Example 1 Solving a Polynomial Inequality Using Its Graph
  607. Example 2 How to Solve a Polynomial Inequality Algebraically
  608. The Role of Multiplicity in Solving Polynomial Inequalities
  609. Solve Rational Inequalities Algebraically and Graphically
  610. Example 3 Solving a Rational Inequality Using Its Graph
  611. Example 4 How to Solve a Rational Inequality Algebraically
  612. The Role of Multiplicity in Solving Rational Inequalities
  613. 4.6 Assess Your Understanding
  614. Concepts and Vocabulary
  615. Skill Building
  616. Applications and Extensions
  617. Explaining Concepts: Discussion and Writing
  618. Chapter Review
  619. Things to Know
  620. Objectives
  621. Review Exercises
  622. Chapter Test
  623. Cumulative Review
  624. Chapter Projects
  625. 5 Exponential and Logarithmic Functions
  626. Outline
  627. A Look Back
  628. A Look Ahead
  629. 5.1 Composite Functions
  630. Objectives
  631. 1 Form a Composite Function
  632. Example 1 Evaluating a Composite Function
  633. Solution
  634. Comment
  635. 2 Find the Domain of a Composite Function
  636. Example 2 Finding a Composite Function and Its Domain
  637. Solution
  638. Example 3 Finding the Domain of f ∘ g
  639. Solution
  640. Example 4 Finding a Composite Function and Its Domain
  641. Solution
  642. Example 5 Showing That Two Composite Functions Are Equal
  643. Solution
  644. Calculus Application
  645. Example 6 Finding the Components of a Composite Function
  646. Solution
  647. Example 7 Finding the Components of a Composite Function
  648. Solution
  649. 5.1 Assess Your Understanding
  650. Concepts and Vocabulary
  651. Skill Building
  652. Applications and Extensions
  653. Retain Your Knowledge
  654. 5.2 One-to-One Functions; Inverse Functions
  655. Objectives
  656. 1 Determine Whether a Function Is One-to-One
  657. Example 1 Determining Whether a Function Is One-to-One
  658. Solution
  659. Example 2 Using the Horizontal-line Test
  660. Solution
  661. 2 Determine the Inverse of a Function Defined by a Map or a Set of Ordered Pairs
  662. Example 3 Finding the Inverse of a Function Defined by a Map
  663. Solution
  664. Example 4 Finding the Inverse of a Function Defined by a Set of Ordered Pairs
  665. Solution
  666. Example 5 Verifying Inverse Functions
  667. Solution
  668. Example 6 Verifying Inverse Functions
  669. Solution
  670. 3 Obtain the Graph of the Inverse Function from the Graph of the Function
  671. Example 7 Graphing the Inverse Function
  672. Solution
  673. 4 Find the Inverse of a Function Defined by an Equation
  674. Example 8 How to Find the Inverse Function
  675. Step-by-Step Solution
  676. Procedure for Finding the Inverse of a One-to-One Function
  677. Example 9 Finding the Inverse Function
  678. Solution
  679. Example 10 Finding the Inverse of a Domain-restricted Function
  680. Solution
  681. Summary
  682. 5.2 Assess Your Understanding
  683. Concepts and Vocabulary
  684. Skill Building
  685. Applications and Extensions
  686. Explaining Concepts: Discussion and Writing
  687. Retain Your Knowledge
  688. 5.3 Exponential Functions
  689. Objectives
  690. 1 Evaluate Exponential Functions
  691. Example 1 Using a Calculator to Evaluate Powers of 2
  692. Solution
  693. Introduction to Exponential Growth
  694. Proof
  695. Example 2 Identifying Linear or Exponential Functions
  696. Solution
  697. 2 Graph Exponential Functions
  698. Example 3 Graphing an Exponential Function
  699. Solution
  700. Properties of the Exponential Function f(x) = ax, a > 1
  701. Example 4 Graphing an Exponential Function
  702. Solution
  703. Properties of the Exponential Function f(x) = ax, 0 < a < 1
  704. Example 5 Graphing Exponential Functions Using Transformations
  705. Solution
  706. 3 Define the Number e
  707. Example 6 Graphing Exponential Functions Using Transformations
  708. Solution
  709. 4 Solve Exponential Equations
  710. Example 7 Solving an Exponential Equation
  711. Algebraic Solution
  712. Graphing Solution
  713. Example 8 Solving an Exponential Equation
  714. Solution
  715. Example 9 Exponential Probability
  716. Solution
  717. Summary
  718. Properties of the Exponential Function
  719. 5.3 Assess Your Understanding
  720. Concepts and Vocabulary
  721. Skill Building
  722. Mixed Practice
  723. Applications and Extensions
  724. Explaining Concepts: Discussion and Writing
  725. Retain Your Knowledge
  726. 5.4 Logarithmic Functions
  727. Objectives
  728. Example 1 Relating Logarithms to Exponents
  729. 1 Change Exponential Statements to Logarithmic Statements and Logarithmic Statements to Exponential Statements
  730. Example 2 Changing Exponential Statements to Logarithmic Statements
  731. Solution
  732. Example 3 Changing Logarithmic Statements to Exponential Statements
  733. Solution
  734. 2 Evaluate Logarithmic Expressions
  735. Example 4 Finding the Exact Value of a Logarithmic Expression
  736. Solution
  737. 3 Determine the Domain of a Logarithmic Function
  738. Example 5 Finding the Domain of a Logarithmic Function
  739. Solution
  740. 4 Graph Logarithmic Functions
  741. Properties of the Logarithmic Function f(x) = loga > 0, a ≠ 1
  742. Example 6 Graphing a Logarithmic Function and Its Inverse
  743. Solution
  744. Example 7 Graphing a Logarithmic Function and Its Inverse
  745. Solution
  746. 5 Solve Logarithmic Equations
  747. Example 8 Solving Logarithmic Equations
  748. Solution
  749. Example 9 Using Logarithms to Solve an Exponential Equation
  750. Solution
  751. Example 10 Alcohol and Driving
  752. Solution
  753. Summary
  754. Properties of the Logarithmic Function
  755. 5.4 Assess Your Understanding
  756. Concepts and Vocabulary
  757. Skill Building
  758. Mixed Practice
  759. Applications and Extensions
  760. Explaining Concepts: Discussion and Writing
  761. Retain Your Knowledge
  762. 5.5 Properties of Logarithms
  763. Objectives
  764. 1 Work with the Properties of Logarithms
  765. Example 1 Establishing Properties of Logarithms
  766. Solution
  767. Proof of Property (1)
  768. Proof of Property (2)
  769. Example 2 Using Properties (1) and (2)
  770. Proof of Property (3)
  771. Proof of Property (5)
  772. Proof of Property (6)
  773. 2 Write a Logarithmic Expression as a Sum or Difference of Logarithms
  774. Example 3 Writing a Logarithmic Expression as a Sum of Logarithms
  775. Example 4 Writing a Logarithmic Expression as a Difference of Logarithms
  776. Solution
  777. Example 5 Writing a Logarithmic Expression as a Sum and Difference of Logarithms
  778. Solution
  779. 3 Write a Logarithmic Expression as a Single Logarithm
  780. Example 6 Writing Expressions as a Single Logarithm
  781. Solution
  782. 4 Evaluate a Logarithm Whose Base Is Neither 10 Nor e
  783. Example 7 Approximating a Logarithm Whose Base Is Neither 10 Nor e
  784. Solution
  785. Proof
  786. Example 8 Using the Change-of-Base Formula
  787. Solution
  788. 5 Graph a Logarithmic Function Whose Base Is Neither 10 Nor e
  789. Example 9 Graphing a Logarithmic Function Whose Base Is Neither 10 Nor e
  790. Solution
  791. Summary
  792. Properties of Logarithms
  793. 5.5 Assess Your Understanding
  794. Concepts and Vocabulary
  795. Skill Building
  796. Mixed Practice
  797. Applications and Extensions
  798. Explaining Concepts: Discussion and Writing
  799. Retain Your Knowledge
  800. 5.6 Logarithmic and Exponential Equations
  801. Objectives
  802. 1 Solve Logarithmic Equations
  803. Example 1 Solving a Logarithmic Equation
  804. Algebraic Solution
  805. Graphing Solution
  806. Example 2 Solving a Logarithmic Equation
  807. Algebraic Solution
  808. Graphing Solution
  809. Example 3 Solving a Logarithmic Equation
  810. Algebraic Solution
  811. Graphing Solution
  812. 2 Solve Exponential Equations
  813. Example 4 Solving an Exponential Equation
  814. Algebraic Solution
  815. Graphing Solution
  816. Example 5 Solving an Exponential Equation
  817. Algebraic Solution
  818. Graphing Solution
  819. Example 6 Solving an Exponential Equation
  820. Algebraic Solution
  821. Graphing Solution
  822. Example 7 Solving an Exponential Equation That Is Quadratic in Form
  823. Algebraic Solution
  824. Graphing Solution
  825. 3 Solve Logarithmic and Exponential Equations Using a Graphing Utility
  826. Example 8 Solving Equations Using a Graphing Utility
  827. Solution
  828. 5.6 Assess Your Understanding
  829. Skill Building
  830. Mixed Practice
  831. Applications and Extensions
  832. Explaining Concepts: Discussion and Writing
  833. Retain Your Knowledge
  834. 5.7 Financial Models
  835. Objectives
  836. 1 Determine the Future Value of a Lump Sum of Money
  837. Example 1 Computing Compound Interest
  838. Solution
  839. Example 2 Comparing Investments Using Different Compounding Periods
  840. Example 3 Using Continuous Compounding
  841. 2 Calculate Effective Rates of Return
  842. Example 4 Computing the Effective Rate of Interest—Which Is the Best Deal?
  843. Solution
  844. 3 Determine the Present Value of a Lump Sum of Money
  845. Example 5 Computing the Value of a Zero-Coupon Bond
  846. Solution
  847. 4 Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money
  848. Example 6 Rate of Interest Required to Double an Investment
  849. Solution
  850. Example 7 Time Required to Double or Triple an Investment
  851. Solution
  852. 5.7 Assess Your Understanding
  853. Concepts and Vocabulary
  854. Skill Building
  855. Applications and Extensions
  856. Inflation
  857. Explaining Concepts: Discussion and Writing
  858. Retain Your Knowledge
  859. 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
  860. Objectives
  861. 1 Find Equations of Populations That Obey the Law of Uninhibited Growth
  862. Uninhibited Growth of Cells
  863. Example 1 Bacterial Growth
  864. Solution
  865. Example 2 Bacterial Growth
  866. Solution
  867. 2 Find Equations of Populations That Obey the Law of Decay
  868. Uninhibited Radioactive Decay
  869. Example 3 Estimating the Age of Ancient Tools
  870. Solution
  871. 3 Use Newton’s Law of Cooling
  872. Newton’s Law of Cooling
  873. Example 4 Using Newton’s Law of Cooling
  874. Solution
  875. 4 Use Logistic Models
  876. Logistic Model
  877. Properties of the Logistic Model, Equation (5)
  878. Example 5 Fruit Fly Population
  879. Solution
  880. Example 6 Wood Products
  881. Solution
  882. 5.8 Assess Your Understanding
  883. Applications and Extensions
  884. Retain Your Knowledge
  885. 5.9 Building Exponential, Logarithmic, and Logistic Models from Data
  886. Objectives
  887. 1 Build an Exponential Model from Data
  888. Example 1 Fitting an Exponential Function to Data
  889. Solution
  890. 2 Build a Logarithmic Model from Data
  891. Example 2 Fitting a Logarithmic Function to Data
  892. Solution
  893. 3 Build a Logistic Model from Data
  894. Example 3 Fitting a Logistic Function to Data
  895. Solution
  896. 5.9 Assess Your Understanding
  897. Applications and Extensions
  898. Mixed Practice
  899. Retain Your Knowledge
  900. Chapter Review
  901. Things to Know
  902. Objectives
  903. Review Exercises
  904. Chapter Test
  905. Cumulative Review
  906. Chapter Projects
  907. 6 Trigonometric Functions
  908. Outline
  909. A Look Back
  910. A Look Ahead
  911. 6.1 Angles and Their Measure
  912. Preparing for This Section
  913. Objectives
  914. Degrees
  915. Example 1 Drawing an Angle
  916. Solution
  917. Convert between Decimal and Degree, Minute, Second Measures for Angles
  918. Example 2 Converting between Degree, Minute, Second, and Decimal Forms
  919. Algebraic Solution
  920. Graphing Solution
  921. Radians
  922. Find the Length of an Arc of a Circle
  923. Example 3 Finding the Length of an Arc of a Circle
  924. Solution
  925. Convert from Degrees to Radians and from Radians to Degrees
  926. Example 4 Converting from Degrees to Radians
  927. Solution
  928. Example 5 Converting from Radians to Degrees
  929. Solution
  930. Example 6 Finding the Distance between Two Cities
  931. Solution
  932. Find the Area of a Sector of a Circle
  933. Example 7 Finding the Area of a Sector of a Circle
  934. Solution
  935. Find the Linear Speed of an Object Traveling in Circular Motion
  936. Example 8 Finding Linear Speed
  937. Solution
  938. 6.1 Assess Your Understanding
  939. Concepts and Vocabulary
  940. Skill Building
  941. Applications and Extensions
  942. Explaining Concepts: Discussion and Writing
  943. 6.2 Trigonometric Functions: Unit Circle Approach
  944. Preparing for This Section
  945. Objectives
  946. The Unit Circle
  947. Find the Exact Values of the Trigonometric Functions Using a Point on the Unit Circle
  948. Example 1 Finding the Values of the Six Trigonometric Functions Using a Point on the Unit Circle
  949. Solution
  950. Trigonometric Functions of Angles
  951. Find the Exact Values of the Trigonometric Functions of Quadrantal Angles
  952. Example 2 Finding the Exact Values of the Six Trigonometric Functions of Quadrantal Angles
  953. Solution
  954. Example 3 Finding Exact Values of the Trigonometric Functions of Angles That Are Integer Multiples of Quadrantal Angles
  955. Solution
  956. Find the Exact Values of the Trigonometric Functions of π4=45∘
  957. Example 4 Find the Exact Values of the Trigonometric Functions of π4=45∘
  958. Solution
  959. Example 5 Finding the Exact Value of a Trigonometric Expression
  960. Solution
  961. Find the Exact Values of the Trigonometric Functions of π6=30∘ and π3=60∘
  962. Example 6 Finding the Exact Values of the Trigonometric Functions of π3=60∘
  963. Solution
  964. Example 7 Finding the Exact Values of the Trigonometric Functions of π6=30∘
  965. Solution
  966. Example 8 Constructing a Rain Gutter
  967. Solution
  968. Find the Exact Values of the Trigonometric Functions for Integer Multiples of π6=30∘,π4=45∘, and π3=60∘
  969. Example 9 Finding Exact Values for Multiples of π4=45∘
  970. Solution
  971. Example 10 Finding Exact Values for Multiples of π6=30∘ or π3=60∘
  972. Use a Calculator to Approximate the Value of a Trigonometric Function
  973. Example 11 Using a Calculator to Approximate the Value of a Trigonometric Function
  974. Solution
  975. Use a Circle of Radius r to Evaluate the Trigonometric Functions
  976. Example 12 Finding the Exact Values of the Six Trigonometric Functions
  977. Solution
  978. 6.2 Assess Your Understanding
  979. Concepts and Vocabulary
  980. Skill Building
  981. Applications and Extensions
  982. Explaining Concepts: Discussion and Writing
  983. 6.3 Properties of the Trigonometric Functions
  984. Preparing for This Section
  985. Objectives
  986. Determine the Domain and the Range of the Trigonometric Functions
  987. Determine the Period of the Trigonometric Functions
  988. Example 1 Finding Exact Values Using Periodic Properties
  989. Solution
  990. Determine the Signs of the Trigonometric Functions in a Given Quadrant
  991. Example 2 Finding the Quadrant in Which an Angle θ Lies
  992. Solution
  993. Find the Values of the Trigonometric Functions Using Fundamental Identities
  994. Example 3 Finding Exact Values Using Identities When Sine and Cosine Are Given
  995. Solution
  996. Example 4 Finding the Exact Value of a Trigonometric Expression Using Identities
  997. Solution
  998. Find the Exact Values of the Trigonometric Functions of an Angle Given One of the Functions and the Quadrant of the Angle
  999. Example 5 Finding Exact Values Given One Value and the Sign of Another
  1000. Option 1 Using a Circle
  1001. Option 2 Using Identities
  1002. Example 6 Given the Value of One Trigonometric Function and the Sign of Another, Find the Values of the Remaining Ones
  1003. Option 1 Using a Circle
  1004. Option 2 Using Identities
  1005. Use Even–Odd Properties to Find the Exact Values of the Trigonometric Functions
  1006. Proof
  1007. Example 7 Finding Exact Values Using Even–Odd Properties
  1008. Solution
  1009. 6.3 Assess Your Understanding
  1010. Concepts and Vocabulary
  1011. Skill Building
  1012. Applications and Extensions
  1013. Explaining Concepts: Discussion and Writing
  1014. 6.4 Graphs of the Sine and Cosine Functions*
  1015. Preparing for This Section
  1016. Objectives
  1017. The Graph of the Sine Function y = sin x
  1018. Graph Functions of the Form y = A sin(ωx) Using Transformations
  1019. Example 1 Graphing Functions of the Form y = A sin(ωx) Using Transformations
  1020. Solution
  1021. Example 2 Graphing Functions of the Form y = A sin(ωx) Using Transformations
  1022. Solution
  1023. The Graph of the Cosine Function y = cos x
  1024. Graph Functions of the Form y = A cos (ωx) Using Transformations
  1025. Example 3 Graphing Functions of the Form y = A cos (ωx) Using Transformations
  1026. Solution
  1027. Sinusoidal Graphs
  1028. Determine the Amplitude and Period of Sinusoidal Functions
  1029. Example 4 Finding the Amplitude and Period of a Sinusoidal Function
  1030. Solution
  1031. Graph Sinusoidal Functions Using Key Points
  1032. Example 5 Graphing a Sinusoidal Function Using Key Points
  1033. Example 6 Graphing a Sinusoidal Function Using Key Points
  1034. Solution
  1035. Example 7 Graphing a Sinusoidal Function Using Key Points
  1036. Solution
  1037. Find an Equation for a Sinusoidal Graph
  1038. Example 8 Finding an Equation for a Sinusoidal Graph
  1039. Solution
  1040. Example 9 Finding an Equation for a Sinusoidal Graph
  1041. Solution
  1042. 6.4 Assess Your Understanding
  1043. Concepts and Vocabulary
  1044. Skill Building
  1045. Applications and Extensions
  1046. Explaining Concepts: Discussion and Writing
  1047. 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
  1048. Preparing for This Section
  1049. Objectives
  1050. The Graph of the Tangent Function y = tan x
  1051. Graph Functions of the Form y = A tan (ωx) + B and y = A cot (ωx) + B
  1052. Example 1 Graphing Functions of the Form y = A tan (ωx) + B
  1053. Solution
  1054. Example 2 Graphing Functions of the Form y = A tan (ωx) + B
  1055. Solution
  1056. The Graph of the Cotangent Function y = cot x
  1057. The Graphs of the Cosecant Function and the Secant Function
  1058. Graph Functions of the Form y = A csc (ωx) + B and y = A sec (ωx) + B
  1059. Example 3 Graphing Functions of the Form y = A csc(ωx) + B
  1060. Solution
  1061. 6.5 Assess Your Understanding
  1062. Concepts and Vocabulary
  1063. Skill Building
  1064. Applications and Extensions
  1065. 6.6 Phase Shift; Sinusoidal Curve Fitting
  1066. Objectives
  1067. Graph Sinusoidal Functions of the Form y = A sin (ωx − ϕ)+ B
  1068. Example 1 Finding the Amplitude, Period, and Phase Shift of a Sinusoidal Function and Graphing It
  1069. Solution
  1070. Example 2 Finding the Amplitude, Period, and Phase Shift of a Sinusoidal Function and Graphing It
  1071. Solution
  1072. Build Sinusoidal Models from Data
  1073. EXAMPLE 3 Finding a Sinusoidal Function from Temperature Data
  1074. Solution
  1075. Example 4 Finding a Sinusoidal Function for Hours of Daylight
  1076. Solution
  1077. Example 5 Finding the Sine Function of Best Fit
  1078. Solution
  1079. 6.6 Assess Your Understanding
  1080. Concepts and Vocabulary
  1081. Skill Building
  1082. Applications and Extensions
  1083. Discussion and Writing
  1084. Chapter Review
  1085. Things to Know
  1086. Objectives
  1087. Review Exercises
  1088. Chapter Test
  1089. Cumulative Review
  1090. Chapter Projects
  1091. 7 Analytic Trigonometry
  1092. Outline
  1093. A Look Back
  1094. A Look Ahead
  1095. 7.1 The Inverse Sine, Cosine, and Tangent Functions
  1096. Preparing For This Section
  1097. Objectives
  1098. The Inverse Sine Function
  1099. 1 Find the Exact Value of an Inverse Sine Function
  1100. Example 1 Finding the Exact Value of an Inverse Sine Function
  1101. Solution
  1102. Example 2 Finding the Exact Value of an Inverse Sine Function
  1103. Solution
  1104. 2 Find an Approximate Value of an Inverse Sine Function
  1105. Example 3 Finding an Approximate Value of an Inverse Sine Function
  1106. Solution
  1107. 3 Use Properties of Inverse Functions to Find Exact Values of Certain Composite Functions
  1108. Example 4 Finding the Exact Value of Certain Composite Functions
  1109. Solution
  1110. Example 5 Finding the Exact Value of Certain Composite Functions
  1111. Solution
  1112. The Inverse Cosine Function
  1113. Example 6 Finding the Exact Value of an Inverse Cosine Function
  1114. Solution
  1115. Example 7 Finding the Exact Value of an Inverse Cosine Function
  1116. Solution
  1117. Example 8 Using Properties of Inverse Functions to Find the Exact Value of Certain Composite Functions
  1118. Solution
  1119. The Inverse Tangent Function
  1120. Example 9 Finding the Exact Value of an Inverse Tangent Function
  1121. Solution
  1122. 4 Find the Inverse Function of a Trigonometric Function
  1123. Example 10 Finding the Inverse Function of a Trigonometric Function
  1124. Solution
  1125. 5 Solve Equations Involving Inverse Trigonometric Functions
  1126. Example 11 Solving an Equation Involving an Inverse Trigonometric Function
  1127. Solution
  1128. 7.1 Assess Your Understanding
  1129. Concepts and Vocabulary
  1130. Skill Building
  1131. Applications and Extensions
  1132. Retain Your Knowledge
  1133. 7.2 The Inverse Trigonometric Functions (Continued)
  1134. Preparing For This Section
  1135. Objectives
  1136. 1 Find the Exact Value of Expressions Involving the Inverse Sine, Cosine, and Tangent Functions
  1137. Example 1 Finding the Exact Value of Expressions Involving Inverse Trigonometric Functions
  1138. Solution
  1139. Example 2 Finding the Exact Value of Expressions Involving Inverse Trigonometric Functions
  1140. Solution
  1141. Example 3 Finding the Exact Value of Expressions Involving Inverse Trigonometric Functions
  1142. Solution
  1143. 2 Define the Inverse Secant, Cosecant, and Cotangent Functions
  1144. Example 4 Finding the Exact Value of an Inverse Cosecant Function
  1145. Solution
  1146. 3 Use a Calculator to Evaluate sec−1 x, csc−1 x, and cot−1 x
  1147. Example 5 Approximating the Value of Inverse Trigonometric Functions
  1148. Solution
  1149. 4 Write a Trigonometric Expression as an Algebraic Expression
  1150. Example 6 Writing a Trigonometric Expression as an Algebraic Expression
  1151. Solution
  1152. 7.2 Assess Your Understanding
  1153. Concepts and Vocabulary
  1154. Skill Building
  1155. Mixed Practice
  1156. Applications and Extensions
  1157. Explaining Concepts: Discussion and Writing
  1158. Retain Your Knowledge
  1159. 7.3 Trigonometric Equations
  1160. Preparing For This Section
  1161. Objectives
  1162. 1 Solve Equations Involving a Single Trigonometric Function
  1163. Example 1 Checking Whether a Given Number Is a Solution of a Trigonometric Equation
  1164. Solution
  1165. Example 2 Finding All the Solutions of a Trigonometric Equation
  1166. Solution
  1167. Example 3 Solving a Linear Trigonometric Equation
  1168. Solution
  1169. Warning
  1170. Example 4 Solving a Trigonometric Equation
  1171. Solution
  1172. Warning
  1173. Example 5 Solving a Trigonometric Equation
  1174. Solution
  1175. 2 Solve Trigonometric Equations Using a Calculator
  1176. Example 6 Solving a Trigonometric Equation with a Calculator
  1177. Solution
  1178. Warning
  1179. 3 Solve Trigonometric Equations Quadratic in Form
  1180. Example 7 Solving a Trigonometric Equation Quadratic in Form
  1181. Solution
  1182. 4 Solve Trigonometric Equations Using Fundamental Identities
  1183. Example 8 Solving a Trigonometric Equation Using Identities
  1184. Solution
  1185. Example 9 Solving a Trigonometric Equation Using Identities
  1186. Solution
  1187. 5 Solve Trigonometric Equations Using a Graphing Utility
  1188. Example 10 Solving a Trigonometric Equation Using a Graphing Utility
  1189. Solution
  1190. 7.3 Assess Your Understanding
  1191. Concepts and Vocabulary
  1192. Skill Building
  1193. Mixed Practice
  1194. Applications and Extensions
  1195. Explaining Concepts: Discussion and Writing
  1196. Retain Your Knowledge
  1197. 7.4 Trigonometric Identities
  1198. Preparing For This Section
  1199. Objectives
  1200. 1 Use Algebra to Simplify Trigonometric Expressions
  1201. Example 1 Using Algebraic Techniques to Simplify Trigonometric Expressions
  1202. Solution
  1203. 2 Establish Identities
  1204. Example 2 Establishing an Identity
  1205. Solution
  1206. Example 3 Establishing an Identity
  1207. Solution
  1208. Example 4 Establishing an Identity
  1209. Solution
  1210. Example 5 Establishing an Identity
  1211. Solution
  1212. Example 6 Establishing an Identity
  1213. Solution
  1214. Example 7 Establishing an Identity
  1215. Solution
  1216. Example 8 Establishing an Identity
  1217. Solution
  1218. 7.4 Assess Your Understanding
  1219. Concepts and Vocabulary
  1220. Skill Building
  1221. Applications and Extensions
  1222. Explaining Concepts: Discussion and Writing
  1223. Retain Your Knowledge
  1224. 7.5 Sum and Difference Formulas
  1225. Preparing For This Section
  1226. Objectives
  1227. Proof
  1228. 1 Use Sum and Difference Formulas to Find Exact Values
  1229. Example 1 Using the Sum Formula to Find an Exact Value
  1230. Solution
  1231. Example 2 Using the Difference Formula to Find an Exact Value
  1232. Solution
  1233. Proof
  1234. Proof
  1235. Example 3 Using the Sum Formula to Find an Exact Value
  1236. Solution
  1237. Example 4 Using the Difference Formula to Find an Exact Value
  1238. Solution
  1239. Example 5 Finding Exact Values
  1240. Solution
  1241. 2 Use Sum and Difference Formulas to Establish Identities
  1242. Example 6 Establishing an Identity
  1243. Solution
  1244. Proof
  1245. Proof
  1246. Example 7 Establishing an Identity
  1247. Solution
  1248. Example 8 Establishing an Identity
  1249. Solution
  1250. 3 Use Sum and Difference Formulas Involving Inverse Trigonometric Functions
  1251. Example 9 Finding the Exact Value of an Expression Involving Inverse Trigonometric Functions
  1252. Solution
  1253. Example 10 Writing a Trigonometric Expression as an Algebraic Expression
  1254. Solution
  1255. 4 Solve Trigonometric Equations Linear in Sine and Cosine
  1256. Example 11 Solving a Trigonometric Equation Linear in Sine and Cosine
  1257. Option 1
  1258. Option 2
  1259. Example 12 Solving a Trigonometric Equation Linear in sin θ and cos θ
  1260. Solution
  1261. 7.5 Assess Your Understanding
  1262. Concepts and Vocabulary
  1263. Skill Building
  1264. Applications and Extensions
  1265. Explaining Concepts: Discussion and Writing
  1266. Retain Your Knowledge
  1267. 7.6 Double-angle and Half-angle Formulas
  1268. Objectives
  1269. 1 Use Double-angle Formulas to Find Exact Values
  1270. Example 1 Finding Exact Values Using the Double-angle Formulas
  1271. Solution
  1272. 2 Use Double-angle Formulas to Establish Identities
  1273. Example 2 Establishing Identities
  1274. Solution
  1275. Example 3 Establishing an Identity
  1276. Solution
  1277. Example 4 Solving a Trigonometric Equation Using Identities
  1278. Solution
  1279. Example 5 Projectile Motion
  1280. Solution
  1281. 3 Use Half-angle Formulas to Find Exact Values
  1282. Example 6 Finding Exact Values Using Half-angle Formulas
  1283. Solution
  1284. Example 7 Finding Exact Values Using Half-angle Formulas
  1285. Solution
  1286. 7.6 Assess Your Understanding
  1287. Concepts and Vocabulary
  1288. Skill Building
  1289. Mixed Practice
  1290. Applications and Extensions
  1291. Explaining Concepts: Discussion and Writing
  1292. Retain Your Knowledge
  1293. 7.7 Product-to-Sum and Sum-to-Product Formulas
  1294. Objectives
  1295. 1 Express Products as Sums
  1296. Example 1 Expressing Products as Sums
  1297. Solution
  1298. 2 Express Sums as Products
  1299. Proof
  1300. Example 2 Expressing Sums (or Differences) as Products
  1301. Solution
  1302. 7.7 Assess Your Understanding
  1303. Skill Building
  1304. Applications and Extensions
  1305. Retain Your Knowledge
  1306. Chapter Review
  1307. Things to Know
  1308. Objectives
  1309. Review Exercises
  1310. Chapter Test
  1311. Cumulative Review
  1312. Chapter Projects
  1313. 8 Applications of Trigonometric Functions
  1314. Outline
  1315. A Look Back
  1316. A Look Ahead
  1317. 8.1 Right Triangle Trigonometry; Applications
  1318. Preparing For This Section
  1319. Objectives
  1320. 1 Find the Value of Trigonometric Functions of Acute Angles Using Right Triangles
  1321. Example 1 Finding the Value of Trigonometric Functions from a Right Triangle
  1322. Solution
  1323. Example 2 Constructing a Rain Gutter
  1324. Solution
  1325. 2 Use the Complementary Angle Theorem
  1326. Example 3 Using the Complementary Angle Theorem
  1327. 3 Solve Right Triangles
  1328. Example 4 Solving a Right Triangle
  1329. Solution
  1330. Example 5 Solving a Right Triangle
  1331. Solution
  1332. 4 Solve Applied Problems*
  1333. Example 6 Finding the Width of a River
  1334. Solution
  1335. Example 7 Finding the Inclination of a Mountain Trail
  1336. Solution
  1337. Example 8 Finding the Height of a Cloud
  1338. Solution
  1339. Example 9 Finding the Height of a Statue on a Building
  1340. Solution
  1341. Example 10 The Gibb’s Hill Lighthouse, Southampton, Bermuda
  1342. Solution
  1343. Example 11 Finding the Bearing of an Object
  1344. Solution
  1345. Example 12 Finding the Bearing of an Airplane
  1346. Solution
  1347. 8.1 Assess Your Understanding
  1348. Concepts and Vocabulary
  1349. Skill Building
  1350. Applications and Extensions
  1351. Explaining Concepts: Discussion and Writing
  1352. Retain Your Knowledge
  1353. 8.2 The Law of Sines
  1354. Preparing For This Section
  1355. Objectives
  1356. 1 Solve SAA or ASA Triangles
  1357. Example 1 Using the Law of Sines to Solve an SAA Triangle
  1358. Solution
  1359. Example 2 Using the Law of Sines to Solve an ASA Triangle
  1360. Solution
  1361. 2 Solve SSA Triangles
  1362. Example 3 Using the Law of Sines to Solve an SSA Triangle (No Solution)
  1363. Solution
  1364. Example 4 Using the Law of Sines to Solve an SSA Triangle (One Solution)
  1365. Solution
  1366. Example 5 Using the Law of Sines to Solve an SSA Triangle (Two Solutions)
  1367. Solution
  1368. 3 Solve Applied Problems
  1369. Example 6 Finding the Height of a Mountain
  1370. Solution
  1371. Example 7 Rescue at Sea
  1372. Solution
  1373. Proof of the Law of Sines
  1374. 8.2 Assess Your Understanding
  1375. Concepts and Vocabulary
  1376. Skill Building
  1377. Applications and Extensions
  1378. Explaining Concepts: Discussion and Writing
  1379. Retain Your Knowledge
  1380. 8.3 The Law of Cosines
  1381. Preparing For This Section
  1382. Objectives
  1383. Proof
  1384. 1 Solve SAS Triangles
  1385. Example 1 Using the Law of Cosines to Solve an SAS Triangle
  1386. Solution
  1387. 2 Solve SSS Triangles
  1388. Example 2 Using the Law of Cosines to Solve an SSS Triangle
  1389. Solution
  1390. 3 Solve Applied Problems
  1391. Example 3 Correcting a Navigational Error
  1392. Solution
  1393. 8.3 Assess Your Understanding
  1394. Concepts and Vocabulary
  1395. Skill Building
  1396. Mixed Practice
  1397. Applications and Extensions
  1398. Explaining Concepts: Discussion and Writing
  1399. Retain Your Knowledge
  1400. 8.4 Area of a Triangle
  1401. Preparing For This Section
  1402. Objectives
  1403. Proof
  1404. 1 Find the Area of SAS Triangles
  1405. Example 1 Finding the Area of an SAS Triangle
  1406. Solution
  1407. 2 Find the Area of SSS Triangles
  1408. Example 2 Finding the Area of an SSS Triangle
  1409. Solution
  1410. Proof of Heron’s Formula
  1411. 8.4 Assess Your Understanding
  1412. Concepts and Vocabulary
  1413. Skill Building
  1414. Applications and Extensions
  1415. Explaining Concepts: Discussion and Writing
  1416. Retain Your Knowledge
  1417. 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
  1418. Preparing For This Section
  1419. Objectives
  1420. 1 Build a Model for an Object in Simple Harmonic Motion
  1421. Example 1 Build a Model for an Object in Harmonic Motion
  1422. Solution
  1423. 2 Analyze Simple Harmonic Motion
  1424. Example 2 Analyzing the Motion of an Object
  1425. Solution
  1426. 3 Analyze an Object in Damped Motion
  1427. Example 3 Analyzing a Damped Vibration Curve
  1428. Solution
  1429. Exploration
  1430. Result
  1431. 4 Graph the Sum of Two Functions
  1432. Example 4 Graphing the Sum of Two Functions
  1433. Solution
  1434. Example 5 Graphing the Sum of Two Sinusoidal Functions
  1435. Solution
  1436. 8.5 Assess Your Understanding
  1437. Concepts and Vocabulary
  1438. Skill Building
  1439. Mixed Practice
  1440. Applications and Extensions
  1441. Explaining Concepts: Discussion and Writing
  1442. Retain Your Knowledge
  1443. Chapter Review
  1444. Things to Know
  1445. Formulas
  1446. Objectives
  1447. Review Exercises
  1448. Chapter Test
  1449. Cumulative Review
  1450. Chapter Projects
  1451. 9 Polar Coordinates; Vectors
  1452. Outline
  1453. A Look Back, A Look Ahead
  1454. 9.1 Polar Coordinates
  1455. Preparing for This Section
  1456. Objectives
  1457. 1 Plot Points Using Polar Coordinates
  1458. Example 1 Plotting Points Using Polar Coordinates
  1459. Solution
  1460. Example 2 Finding Several Polar Coordinates of a Single Point
  1461. Example 3 Finding Other Polar Coordinates of a Given Point
  1462. Solution
  1463. 2 Convert from Polar Coordinates to Rectangular Coordinates
  1464. Proof
  1465. Example 4 Converting from Polar Coordinates to Rectangular Coordinates
  1466. Solution
  1467. 3 Convert from Rectangular Coordinates to Polar Coordinates
  1468. Example 5 How to Convert from Rectangular Coordinates to Polar Coordinates with the Point on a Coordinate Axis
  1469. Step-by-Step Solution
  1470. Example 6 How to Convert from Rectangular Coordinates to Polar Coordinates with the Point in a Quadrant
  1471. Step-by-Step Solution
  1472. Example 7 Converting from Rectangular Coordinates to Polar Coordinates
  1473. Solution
  1474. 4 Transform Equations between Polar and Rectangular Forms
  1475. Example 8 Transforming an Equation from Polar to Rectangular Form
  1476. Solution
  1477. Example 9 Transforming an Equation from Rectangular to Polar Form
  1478. Solution
  1479. 9.1 Assess Your Understanding
  1480. Concepts and Vocabulary
  1481. Skill Building
  1482. Applications and Extensions
  1483. Explaining Concepts: Discussion and Writing
  1484. Retain Your Knowledge
  1485. 9.2 Polar Equations and Graphs
  1486. Preparing for This Section
  1487. Objectives
  1488. 1 Identify and Graph Polar Equations by Converting to Rectangular Equations
  1489. Example 1 Identifying and Graphing a Polar Equation (Circle)
  1490. Solution
  1491. Example 2 Identifying and Graphing a Polar Equation (Line)
  1492. Solution
  1493. Example 3 Identifying and Graphing a Polar Equation (Horizontal Line)
  1494. Solution
  1495. 2 Graph Polar Equations Using a Graphing Utility
  1496. Example 4 Graphing a Polar Equation Using a Graphing Utility
  1497. Solution
  1498. Example 5 Identifying and Graphing a Polar Equation (Vertical Line)
  1499. Solution
  1500. Example 6 Identifying and Graphing a Polar Equation (Circle)
  1501. Solution
  1502. Example 7 Identifying and Graphing a Polar Equation (Circle)
  1503. Solution
  1504. Exploration
  1505. 3 Test Polar Equations for Symmetry
  1506. 4 Graph Polar Equations by Plotting Points
  1507. Example 8 Graphing a Polar Equation (Cardioid)
  1508. Solution
  1509. Exploration
  1510. Example 9 Graphing a Polar Equation (Limaçon without Inner Loop)
  1511. Solution
  1512. Exploration
  1513. Example 10 Graphing a Polar Equation (Limaçon with Inner Loop)
  1514. Solution
  1515. Exploration
  1516. Example 11 Graphing a Polar Equation (Rose)
  1517. Solution
  1518. Exploration
  1519. Example 12 Graphing a Polar Equation (Lemniscate)
  1520. Solution
  1521. Example 13 Graphing a Polar Equation (Spiral)
  1522. Solution
  1523. Classification of Polar Equations
  1524. Sketching Quickly
  1525. Example 14 Sketching the Graph of a Polar Equation Quickly
  1526. Solution
  1527. Calculus Comment
  1528. 9.2 Assess Your Understanding
  1529. Concepts and Vocabulary
  1530. Skill Building
  1531. Mixed Practice
  1532. Applications and Extensions
  1533. Explaining Concepts: Discussion and Writing
  1534. Retain Your Knowledge
  1535. 9.3 The Complex Plane; De Moivre’s Theorem
  1536. Preparing for This Section
  1537. Objectives
  1538. 1 Plot Points in the Complex Plane
  1539. Example 1 Plotting a Point in the Complex Plane
  1540. Solution
  1541. 2 Convert a Complex Number between Rectangular Form and Polar Form
  1542. Example 2 Writing a Complex Number in Polar Form
  1543. Solution
  1544. Example 3 Plotting a Point in the Complex Plane and Converting from Polar to Rectangular Form
  1545. Solution
  1546. 3 Find Products and Quotients of Complex Numbers in Polar Form
  1547. Proof
  1548. Example 4 Finding Products and Quotients of Complex Numbers in Polar Form
  1549. Solution
  1550. 4 Use De Moivre’s Theorem
  1551. Example 5 Using De Moivre’s Theorem
  1552. Solution
  1553. Example 6 Using De Moivre’s Theorem
  1554. Algebraic Solution
  1555. Graphing Solution
  1556. 5 Find Complex Roots
  1557. Theorem Finding Complex Roots
  1558. Proof (Outline)
  1559. Example 7 Finding Complex Cube Roots
  1560. Solution
  1561. Historical Problems
  1562. 9.3 Assess Your Understanding
  1563. Concepts and Vocabulary
  1564. Skill Building
  1565. Applications and Extensions
  1566. Retain Your Knowledge
  1567. 9.4 Vectors
  1568. Objectives
  1569. Geometric Vectors
  1570. Adding Vectors Geometrically
  1571. Multiplying Vectors by Numbers Geometrically
  1572. 1 Graph Vectors
  1573. Example 1 Graphing Vectors
  1574. Solution
  1575. Magnitude of Vectors
  1576. 2 Find a Position Vector
  1577. Example 2 Finding a Position Vector
  1578. Solution
  1579. 3 Add and Subtract Vectors Algebraically
  1580. Example 3 Adding and Subtracting Vectors
  1581. Solution
  1582. 4 Find a Scalar Multiple and the Magnitude of a Vector
  1583. Example 4 Finding Scalar Multiples and Magnitudes of Vectors
  1584. Solution
  1585. 5 Find a Unit Vector
  1586. Proof
  1587. Example 5 Finding a Unit Vector
  1588. Solution
  1589. 6 Find a Vector from Its Direction and Magnitude
  1590. Example 6 Finding a Vector When Its Magnitude and Direction Are Given
  1591. Solution
  1592. Example 7 Finding the Direction Angle of a Vector
  1593. Solution
  1594. 7 Model with Vectors
  1595. Example 8 Finding the Actual Speed and Direction of an Aircraft
  1596. Solution
  1597. Example 9 Finding the Weight of a Piano
  1598. Solution
  1599. Example 10 Analyzing an Object in Static Equilibrium
  1600. Solution
  1601. 9.4 Assess Your Understanding
  1602. Concepts and Vocabulary
  1603. Skill Building
  1604. Applications and Extensions
  1605. Explaining Concepts: Discussion and Writing
  1606. Retain Your Knowledge
  1607. 9.5 The Dot Product
  1608. Preparing for This Section
  1609. Objectives
  1610. 1 Find the Dot Product of Two Vectors
  1611. Example 1 Finding Dot Products
  1612. Solution
  1613. Proof
  1614. 2 Find the Angle between Two Vectors
  1615. Example 2 Finding the Angle θ between Two Vectors
  1616. Solution
  1617. 3 Determine Whether Two Vectors Are Parallel
  1618. Example 3 Determining Whether Two Vectors Are Parallel
  1619. 4 Determine Whether Two Vectors Are Orthogonal
  1620. Theorem
  1621. Example 4 Determining Whether Two Vectors Are Orthogonal
  1622. 5 Decompose a Vector into Two Orthogonal Vectors
  1623. Example 5 Decomposing a Vector into Two Orthogonal Vectors
  1624. Solution
  1625. Example 6 Finding the Force Required to Hold a Wagon on a Hill
  1626. Solution
  1627. 6 Compute Work
  1628. Example 7 Computing Work
  1629. Solution
  1630. 9.5 Assess Your Understanding
  1631. Concepts and Vocabulary
  1632. Skill Building
  1633. Applications and Extensions
  1634. Explaining Concepts: Discussion and Writing
  1635. Retain Your Knowledge
  1636. 9.6 Vectors in Space
  1637. Preparing for This Section
  1638. Objectives
  1639. Rectangular Coordinates in Space
  1640. 1 Find the Distance between Two Points in Space
  1641. Example 1 Using the Distance Formula
  1642. Solution
  1643. 2 Find Position Vectors in Space
  1644. Example 2 Finding a Position Vector
  1645. Solution
  1646. 3 Perform Operations on Vectors
  1647. Example 3 Adding and Subtracting Vectors
  1648. Solution
  1649. Example 4 Finding Scalar Products and Magnitudes
  1650. Solution
  1651. Example 5 Finding a Unit  Vector
  1652. Solution
  1653. 4 Find the Dot Product
  1654. Example 6 Finding Dot Products
  1655. Solution
  1656. 5 Find the Angle between Two Vectors
  1657. Example 7 Finding the Angle between Two Vectors
  1658. Solution
  1659. 6 Find the Direction Angles of a Vector
  1660. Example 8 Finding the Direction Angles of a Vector
  1661. Solution
  1662. Example 9 Finding a Direction Angle of a Vector
  1663. Solution
  1664. Example 10 Writing a Vector in Terms of Its Magnitude and Direction Cosines
  1665. Solution
  1666. 9.6 Assess Your Understanding
  1667. Concepts and Vocabulary
  1668. Skill Building
  1669. Applications and Extensions
  1670. Retain Your Knowledge
  1671. 9.7 The Cross Product
  1672. Objectives
  1673. 1 Find the Cross Product of Two Vectors
  1674. Example 1 Finding a Cross Product Using Equation (1)
  1675. Solution
  1676. Example 2 Evaluating Determinants
  1677. Example 3 Using Determinants to Find Cross Products
  1678. Solution
  1679. 2 Know Algebraic Properties of the Cross Product
  1680. Proof
  1681. 3 Know Geometric Properties of the Cross Product
  1682. Proof of Property (8)
  1683. 4 Find a Vector Orthogonal to Two Given Vectors
  1684. Example 4 Finding a Vector Orthogonal to Two Given Vectors
  1685. Solution
  1686. 5 Find the Area of a Parallelogram
  1687. Example 5 Finding the Area of a Parallelogram
  1688. Solution
  1689. 9.7 Assess Your Understanding
  1690. Concepts and Vocabulary
  1691. Skill Building
  1692. Applications and Extensions
  1693. Discussion and Writing
  1694. Retain Your Knowledge
  1695. Chapter Review
  1696. Objectives
  1697. Review Exercises
  1698. Chapter Test
  1699. Chapter Test Prep Videos
  1700. Cumulative Review
  1701. Chapter Projects
  1702. 10 Analytic Geometry
  1703. Outline
  1704. A Look Back
  1705. A Look Ahead
  1706. 10.1 Conics
  1707. Objectives
  1708. 1 Know the Names of the Conics
  1709. 10.2 The Parabola
  1710. Preparing for This Section
  1711. Objectives
  1712. 1 Analyze Parabolas with Vertex at the Origin
  1713. Example 1 Finding the Equation of a Parabola and Graphing It
  1714. Solution
  1715. Example 2 Graphing a Parabola Using a Graphing Utility
  1716. Solution
  1717. Example 3 Analyzing the Equation of a Parabola
  1718. Solution
  1719. Example 4 Analyzing the Equation of a Parabola
  1720. Solution
  1721. Example 5 Finding the Equation of a Parabola
  1722. Solution
  1723. Example 6 Finding the Equation of a Parabola
  1724. Solution
  1725. 2 Analyze Parabolas with Vertex at (h, k)
  1726. Example 7 Finding the Equation of a Parabola, Vertex Not at the Origin
  1727. Solution
  1728. Example 8 Using a Graphing Utility to Graph a Parabola, Vertex Not at Origin
  1729. Solution
  1730. Example 9 Analyzing the Equation of a Parabola
  1731. Solution
  1732. 3 Solve Applied Problems Involving Parabolas
  1733. Example 10 Satellite Dish
  1734. Solution
  1735. 10.2 Assess Your Understanding
  1736. Concepts and Vocabulary
  1737. Skill Building
  1738. Applications and Extensions
  1739. Retain Your Knowledge
  1740. 10.3 The Ellipse
  1741. Preparing for This Section
  1742. Objectives
  1743. 1 Analyze Ellipses with Center at the Origin
  1744. Example 1 Finding an Equation of an Ellipse
  1745. Solution
  1746. Example 2 Graphing an Ellipse Using a Graphing Utility
  1747. Solution
  1748. Example 3 Analyzing the Equation of an Ellipse
  1749. Solution
  1750. Example 4 Analyzing the Equation of an Ellipse
  1751. Solution
  1752. Example 5 Finding an Equation of an Ellipse
  1753. Solution
  1754. 2 Analyze Ellipses with Center at (h, k)
  1755. Example 6 Finding an Equation of an Ellipse, Center Not at the Origin
  1756. Solution
  1757. Example 7 Using a Graphing Utility to Graph an Ellipse, Center Not at the Origin
  1758. Solution
  1759. Example 8 Analyzing the Equation of an Ellipse
  1760. Solution
  1761. 3Solve Applied Problems Involving Ellipses
  1762. Example 9 A Whispering Gallery
  1763. Solution
  1764. 10.3 Assess Your Understanding
  1765. Concepts and Vocabulary
  1766. Skill Building
  1767. Applications and Extensions
  1768. Explaining Concepts: Discussion and Writing
  1769. Retain Your Knowledge
  1770. 10.4 The Hyperbola
  1771. Preparing for This Section
  1772. Objectives
  1773. 1 Analyze Hyperbolas with Center at the Origin
  1774. Example 1 Finding and Graphing an Equation of a Hyperbola
  1775. Solution
  1776. Example 2 Using a Graphing Utility to Graph a Hyperbola
  1777. Solution
  1778. Example 3 Analyzing the Equation of a Hyperbola
  1779. Solution
  1780. Theorem Equation of a Hyperbola; Center at (0, 0) Transverse Axis along the y-Axis
  1781. Example 4 Analyzing the Equation of a Hyperbola
  1782. Solution
  1783. Example 5 Finding an Equation of a Hyperbola
  1784. Solution
  1785. 2 Find the Asymptotes of a Hyperbola
  1786. Proof
  1787. Example 6 Analyzing the Equation of a Hyperbola
  1788. Solution
  1789. Example 7 Analyzing the Equation of a Hyperbola
  1790. Solution
  1791. 3 Analyze Hyperbolas with Center at (h, k)
  1792. Example 8 Finding an Equation of a Hyperbola, Center Not at the Origin
  1793. Solution
  1794. Example 9 Analyzing the Equation of a Hyperbola
  1795. Solution
  1796. 4 Solve Applied Problems Involving Hyperbolas
  1797. Example 10 Lightning Strikes
  1798. Solution
  1799. 10.4 Assess Your Understanding
  1800. Concepts and Vocabulary
  1801. Skill Building
  1802. Mixed Practice
  1803. Applications and Extensions
  1804. Retain Your Knowledge
  1805. 10.5 Rotation of Axes; General Form of a Conic
  1806. PREPARING FOR THIS SECTION
  1807. Objectives
  1808. 1 Identify a Conic
  1809. Proof
  1810. Example 1 Identifying a Conic without Completing the Squares
  1811. Solution
  1812. 2 Use a Rotation of Axes to Transform Equations
  1813. Example 2 Rotating Axes
  1814. Solution
  1815. 3 Analyze an Equation Using a Rotation of Axes
  1816. Example 3 Analyzing an Equation Using a Rotation of Axes
  1817. Solution
  1818. Example 4 Analyzing an Equation Using a Rotation of Axes
  1819. Solution
  1820. 4 Identify Conics without a Rotation of Axes
  1821. Example 5 Identifying a Conic without a Rotation of Axes
  1822. Solution
  1823. 10.5 Assess Your Understanding
  1824. Concepts and Vocabulary
  1825. Skill Building
  1826. Applications and Extensions
  1827. Explaining Concepts: Discussion and Writing
  1828. Retain Your Knowledge
  1829. 10.6 Polar Equations of Conics
  1830. PREPARING FOR THIS SECTION
  1831. Objectives
  1832. 1 Analyze and Graph Polar Equations of Conics
  1833. Example 1 Analyzing and Graphing the Polar Equation of a Conic
  1834. Solution
  1835. Exploration
  1836. Example 2 Analyzing and Graphing the Polar Equation of a Conic
  1837. Solution
  1838. Example 3 Analyzing and Graphing the Polar Equation of a Conic
  1839. Solution
  1840. 2 Convert the Polar Equation of a Conic to a Rectangular Equation
  1841. Example 4 Converting a Polar Equation to a Rectangular Equation
  1842. Solution
  1843. 10.6 Assess Your Understanding
  1844. Concepts and Vocabulary
  1845. Skill Building
  1846. Applications and Extensions
  1847. Retain Your Knowledge
  1848. 10.7 Plane Curves and Parametric Equations
  1849. PREPARING FOR THIS SECTION
  1850. Objectives
  1851. 1 Graph Parametric Equations by Hand
  1852. Example 1 Graphing a Curve Defined by Parametric Equations
  1853. Solution
  1854. 2Graph Parametric Equations Using a Graphing Utility
  1855. Example 2 Graphing a Curve Defined by Parametric Equations Using a Graphing Utility
  1856. Solution
  1857. Exploration
  1858. 3 Find a Rectangular Equation for a Curve Defined Parametrically
  1859. Example 3 Finding the Rectangular Equation of a Curve Defined Parametrically
  1860. Solution
  1861. Example 4 Describing Parametric Equations
  1862. Solution
  1863. 4 Use Time as a Parameter in Parametric Equations
  1864. Example 5 Projectile Motion
  1865. Solution
  1866. Exploration
  1867. Example 6 Simulating Motion
  1868. Solution
  1869. 5 Find Parametric Equations for Curves Defined by Rectangular Equations
  1870. Example 7 Finding Parametric Equations for a Curve Defined by a Rectangular Equation
  1871. Solution
  1872. Example 8 Finding Parametric Equations for an Object in Motion
  1873. Solution
  1874. The Cycloid
  1875. Applications to Mechanics
  1876. 10.7 Assess Your Understanding
  1877. Concepts and Vocabulary
  1878. Skill Building
  1879. Applications and Extensions
  1880. Explaining Concepts: Discussion and Writing
  1881. Retain Your Knowledge
  1882. Chapter Review
  1883. Things to Know
  1884. Objectives
  1885. Review Exercises
  1886. Chapter Test
  1887. Cumulative Review
  1888. Chapter Projects
  1889. 11 Systems of Equations and Inequalities
  1890. Outline
  1891. A Look Back
  1892. A Look Ahead
  1893. 11.1 Systems of Linear Equations: Substitution and Elimination
  1894. Objectives
  1895. Example 1 Movie Theater Ticket Sales
  1896. Solution
  1897. Example 2 Examples of Systems of Equations
  1898. Example 3 Solving a System of Linear Equations Using a Graphing Utility
  1899. Solution
  1900. 1 Solve Systems of Equations by Substitution
  1901. Example 4 How to Solve a System of Linear Equations by Substitution
  1902. Step-by-Step Solution
  1903. 2 Solve Systems of Equations by Elimination
  1904. Example 5 How to Solve a System of Linear Equations by Elimination
  1905. Step-by-Step Solution
  1906. Example 6 Movie Theater Ticket Sales
  1907. Solution
  1908. 3 Identify Inconsistent Systems of Equations Containing Two Variables
  1909. Example 7 An Inconsistent System of Linear Equations
  1910. Solution
  1911. 4 Express the Solution of a System of Dependent Equations Containing Two Variables
  1912. Example 8 Solving a System of Dependent Equations
  1913. Solution
  1914. 5 Solve Systems of Three Equations Containing Three Variables
  1915. Example 9 Solving a System of Three Linear Equations with Three Variables
  1916. Solution
  1917. 6 Identify Inconsistent Systems of Equations Containing Three Variables
  1918. Example 10 Identify an Inconsistent System of Linear Equations
  1919. Solution
  1920. 7 Express the Solution of a System of Dependent Equations Containing Three Variables
  1921. Example 11 Solving a System of Dependent Equations
  1922. Solution
  1923. Example 12 Curve Fitting
  1924. Solution
  1925. 11.1 Assess Your Understanding
  1926. Concepts and Vocabulary
  1927. Skill Building
  1928. Applications and Extensions
  1929. Explaining Concepts: Discussion and Writing
  1930. Retain Your Knowledge
  1931. 11.2 Systems of Linear Equations: Matrices
  1932. Objectives
  1933. Definition
  1934. 1 Write the Augmented Matrix of a System of Linear Equations
  1935. Example 1 Writing the Augmented Matrix of a System of Linear Equations
  1936. Solution
  1937. 2 Write the System of Equations from the Augmented Matrix
  1938. Example 2 Writing the System of Linear Equations from the Augmented Matrix
  1939. Solution
  1940. 3 Perform Row Operations on a Matrix
  1941. Example 3 Applying a Row Operation to an Augmented Matrix
  1942. Solution
  1943. Example 4 Finding a Particular Row Operation
  1944. Solution
  1945. 4 Solve a System of Linear Equations Using Matrices
  1946. Definition
  1947. Example 5 How to Solve a System of Linear Equations Using Matrices
  1948. Step-by-Step Solution
  1949. Example 6 Solving a System of Linear Equations Using Matrices (Row Echelon Form)
  1950. Algebraic Solution
  1951. Graphing Solution
  1952. Example 7 Solving a Dependent System of Linear Equations Using Matrices
  1953. Solution
  1954. Example 8 Solving an Inconsistent System of Linear Equations Using Matrices
  1955. Solution
  1956. Example 9 Solving a System of Linear Equations Using Matrices
  1957. Solution
  1958. Example 10 Financial Planning
  1959. Solution
  1960. 11.2 Assess Your Understanding
  1961. Concepts and Vocabulary
  1962. Skill Building
  1963. Applications and Extensions
  1964. Explaining Concepts: Discussion and Writing
  1965. Retain Your Knowledge
  1966. 11.3 Systems of Linear Equations: Determinants
  1967. Objectives
  1968. 1 Evaluate 2 by 2 Determinants
  1969. Example 1 Evaluating a 2 by 2 Determinant
  1970. Algebraic Solution
  1971. Graphing Solution
  1972. 2 Use Cramer’s Rule to Solve a System of Two Equations Containing Two Variables
  1973. Example 2 Solving a System of Linear Equations Using Determinants
  1974. Algebraic Solution
  1975. Graphing Solution
  1976. 3 Evaluate 3 by 3 Determinants
  1977. Example 3 Finding Minors of a 3 by 3 Determinant
  1978. Solution
  1979. Example 4 Evaluating a 3 by 3 Determinant
  1980. Solution
  1981. 4 Use Cramer’s Rule to Solve a System of Three Equations Containing Three Variables
  1982. Example 5 Using Cramer’s Rule
  1983. Solution
  1984. 5 Know Properties of Determinants
  1985. Theorem
  1986. Proof for 2 by 2 Determinants
  1987. Example 6 Demonstrating Theorem (11)
  1988. Proof
  1989. Example 7 Demonstrating Theorem (13)
  1990. Example 8 Demonstrating Theorem (14)
  1991. Example 9 Demonstrating Theorem (15)
  1992. 11.3 Assess Your Understanding
  1993. Concepts and Vocabulary
  1994. Skill Building
  1995. Mixed Practice
  1996. Applications and Extensions
  1997. Retain Your Knowledge
  1998. 11.4 Matrix Algebra
  1999. Objectives
  2000. Definition
  2001. Example 1 Arranging Data in a Matrix
  2002. Example 2 Examples of Matrices
  2003. 1 Find the Sum and Difference of Two Matrices
  2004. Definition
  2005. Example 3 Adding and Subtracting Matrices
  2006. Algebraic Solution
  2007. Graphing Solution
  2008. Example 4 Demonstrating the Commutative Property
  2009. 2 Find Scalar Multiples of a Matrix
  2010. Example 5 Operations Using Matrices
  2011. Algebraic Solution
  2012. Graphing Solution
  2013. 3 Find the Product of Two Matrices
  2014. Definition
  2015. Example 6 The Product of a Row Vector and a Column Vector
  2016. Example 7 Using Matrices to Compute Revenue
  2017. Solution
  2018. Example 8 Multiplying Two Matrices
  2019. Solution
  2020. Algebraic Solution
  2021. Graphing Solution
  2022. Example 9 Multiplying Two Matrices
  2023. Solution
  2024. Example 10 Multiplying Two Square Matrices
  2025. Solution
  2026. Theorem
  2027. Example 11 Multiplication with an Identity Matrix
  2028. Solution
  2029. 4 Find the Inverse of a Matrix
  2030. Definition
  2031. Example 12 Multiplying a Matrix by Its Inverse
  2032. Solution
  2033. Example 13 Finding the Inverse of a Matrix
  2034. Algebraic Solution
  2035. Graphing Solution
  2036. Example 14 Showing That a Matrix Has No Inverse
  2037. Algebraic Solution
  2038. Graphing Solution
  2039. Seeing the Concept
  2040. 5 Solve a System of Linear Equations Using an Inverse Matrix
  2041. Example 15 Using the Inverse Matrix to Solve a System of Linear Equations
  2042. Solution
  2043. Algebraic Solution
  2044. Graphing Solution
  2045. 11.4 Assess Your Understanding
  2046. Concepts and Vocabulary
  2047. Skill Building
  2048. Mixed Practice
  2049. Applications and Extensions
  2050. Explaining Concepts: Discussion and Writing
  2051. Retain Your Knowledge
  2052. 11.5 Partial Fraction Decomposition
  2053. Objectives
  2054. 1 Decompose PQ Where Q Has Only Nonrepeated Linear Factors
  2055. Example 1 Nonrepeated Linear Factors
  2056. Solution
  2057. 2 Decompose PQ Where Q Has Repeated Linear Factors Case 2: Q has repeated linear factors.
  2058. Example 2 Repeated Linear Factors
  2059. Solution
  2060. Example 3 Repeated Linear Factors
  2061. Solution
  2062. 3 Decompose PQ Where Q Has a Nonrepeated Irreducible Quadratic Factor
  2063. Example 4 Nonrepeated Irreducible Quadratic Factor
  2064. Solution
  2065. 4 Decompose PQ Where Q Has a Repeated Irreducible Quadratic Factor Case 4: Q contains a repeated irreducible quadratic factor.
  2066. Example 5 Repeated Irreducible Quadratic Factor
  2067. Solution
  2068. 11.5 Assess Your Understanding
  2069. Skill Building
  2070. Mixed Practice
  2071. Retain Your Knowledge
  2072. 11.6 Systems of Nonlinear Equations
  2073. Objectives
  2074. 1 Solve a System of Nonlinear Equations Using Substitution
  2075. Example 1 Solving a System of Nonlinear Equations
  2076. Algebraic Solution Using Substitution
  2077. Graphing Solution
  2078. 2 Solve a System of Nonlinear Equations Using Elimination
  2079. Example 2 Solving a System of Nonlinear Equations
  2080. Algebraic Solution Using Elimination
  2081. Graphing Solution
  2082. Example 3 Solving a System of Nonlinear Equations
  2083. Algebraic Solution Using Substitution
  2084. Graphing Solution
  2085. Example 4 Solving a System of Nonlinear Equations
  2086. Algebraic Solution Using Elimination
  2087. Graphing Solution
  2088. Example 5 Solving a System of Nonlinear Equations
  2089. Algebraic Solution
  2090. Graphing Solution
  2091. Example 6 Running a Long-Distance Race
  2092. Solution
  2093. Historical Problem
  2094. 11.6 Assess Your Understanding
  2095. Skill Building
  2096. Mixed Practice
  2097. Applications and Extensions
  2098. Explaining Concepts: Discussion and Writing
  2099. Retain Your Knowledge
  2100. 11.7 Systems of Inequalities
  2101. Objectives
  2102. Example 1 Examples of Inequalities in Two Variables
  2103. 1 Graph an Inequality by Hand
  2104. Example 2 Graphing an Inequality by Hand
  2105. Solution
  2106. Example 3 Graphing an Inequality by Hand
  2107. Solution
  2108. Example 4 Graphing Linear Inequalities by Hand
  2109. Solution
  2110. 2 Graph an Inequality Using a Graphing Utility
  2111. Example 5 Graphing an Inequality Using a Graphing Utility
  2112. Solution
  2113. 3 Graph a System of Inequalities
  2114. Example 6 Graphing a System of Linear Inequalities by Hand
  2115. Solution
  2116. Example 7 Graphing a System of Linear Inequalities Using a Graphing Utility
  2117. Solution
  2118. Example 8 Graphing a System of Linear Inequalities by Hand
  2119. Solution
  2120. Example 9 Graphing a System of Linear Inequalities by Hand
  2121. Solution
  2122. Example 10 Graphing a System of Nonlinear Inequalities by Hand
  2123. Solution
  2124. Example 11 Graphing a System of Four Linear Inequalities by Hand
  2125. Solution
  2126. Example 11 Financial Planning
  2127. Solution
  2128. 11.7 Assess Your Understanding
  2129. Concepts and Vocabulary
  2130. Skill Building
  2131. Applications and Extensions
  2132. Retain Your Knowledge
  2133. 11.8 Linear Programming
  2134. Objectives
  2135. 1 Set Up a Linear Programming Problem
  2136. Example 1 Financial Planning
  2137. Solution
  2138. Definition
  2139. 2 Solve a Linear Programming Problem
  2140. Example 2 Analyzing a Linear Programming Problem
  2141. Solution
  2142. Definition
  2143. Theorem Location of the Solution of a Linear Programming Problem
  2144. Example 3 Solving a Minimum Linear Programming Problem
  2145. Solution
  2146. Example 4 Maximizing Profit
  2147. Solution
  2148. 11.8 Assess Your Understanding
  2149. Concepts and Vocabulary
  2150. Skill Building
  2151. Applications and Extensions
  2152. Explaining Concepts: Discussion and Writing
  2153. Retain Your Knowledge
  2154. Chapter Review
  2155. Things to Know
  2156. Systems of equations (pp. 724–726)
  2157. Matrix (p. 739)
  2158. Determinants and Cramer’s Rule (pp. 755, 757, 758–759, and 760)
  2159. Matrix (p. 765)
  2160. Linear programming problem (p. 810)
  2161. Location of solution (p. 812)
  2162. Objectives
  2163. Review Exercises
  2164. Chapter Test
  2165. Chapter Test Prep Videos
  2166. Cumulative Review
  2167. Chapter Projects
  2168. 12 Sequences; Induction; the Binomial Theorem
  2169. Outline
  2170. A Look Back, A Look Ahead
  2171. 12.1 Sequences
  2172. Preparing for This Section
  2173. Objectives
  2174. Write the First Several Terms of a Sequence
  2175. Example 1 Writing the First Several Terms of a Sequence
  2176. Algebraic Solution
  2177. Graphing Solution
  2178. Example 2 Writing the First Several Terms of a Sequence
  2179. Solution
  2180. Example 3 Writing the First Several Terms of a Sequence
  2181. Solution
  2182. Example 4 Determining a Sequence from a Pattern
  2183. The Factorial Symbol
  2184. Exploration
  2185. Write the Terms of a Sequence Defined by a Recursive Formula
  2186. Example 5 Writing the Terms of a Recursively Defined Sequence
  2187. Algebraic Solution
  2188. Graphing Solution
  2189. Example 6 Writing the Terms of a Recursively Defined Sequence
  2190. Solution
  2191. Use Summation Notation
  2192. Example 7 Expanding Summation Notation
  2193. Solution
  2194. Example 8 Writing a Sum in Summation Notation
  2195. Solution
  2196. Find the Sum of a Sequence Algebraically and Using a Graphing Utility
  2197. Example 9 Finding the Sum of a Sequence
  2198. Algebraic Solution
  2199. Graphing Solution
  2200. Solve Annuity and Amortization Problems
  2201. Example 10 Saving for Spring Break
  2202. Solution
  2203. Example 11 Mortgage Payments
  2204. Solution
  2205. 12.1 Assess Your Understanding
  2206. Concepts and Vocabulary
  2207. Skill Building
  2208. Applications and Extensions
  2209. Explaining Concepts: Discussion and Writing
  2210. 12.2 Arithmetic Sequences
  2211. Objectives
  2212. Determine Whether a Sequence Is Arithmetic
  2213. Example 1 Determining Whether a Sequence Is Arithmetic
  2214. Example 2 Determining Whether a Sequence Is Arithmetic
  2215. Solution
  2216. Example 3 Determining Whether a Sequence Is Arithmetic
  2217. Solution
  2218. Find a Formula for an Arithmetic Sequence
  2219. Example 4 Finding a Particular Term of an Arithmetic Sequence
  2220. Solution
  2221. Example 5 Finding a Recursive Formula for an Arithmetic Sequence
  2222. Solution
  2223. Exploration
  2224. Find the Sum of an Arithmetic Sequence
  2225. Proof
  2226. Example 6 Finding the Sum of an Arithmetic Sequence
  2227. Solution
  2228. Example 7 Finding the Sum of an Arithmetic Sequence
  2229. Solution
  2230. Example 8 Creating a Floor Design
  2231. Solution
  2232. 12.2 Assess Your Understanding
  2233. Concepts and Vocabulary
  2234. Skill Building
  2235. Applications and Extensions
  2236. Explaining Concepts: Discussion and Writing
  2237. 12.3 Geometric Sequences; Geometric Series
  2238. Objectives
  2239. Determine Whether a Sequence Is Geometric
  2240. Example 1 Determining Whether a Sequence Is Geometric
  2241. Example 2 Determining Whether a Sequence Is Geometric
  2242. Solution
  2243. Example 3 Determining Whether a Sequence Is Geometric
  2244. Solution
  2245. Find a Formula for a Geometric Sequence
  2246. Example 4 Finding a Particular Term of a Geometric Sequence
  2247. Solution
  2248. Exploration
  2249. Find the Sum of a Geometric Sequence
  2250. Proof
  2251. Example 5 Finding the Sum of the First n Terms of a Geometric Sequence
  2252. Solution
  2253. Example 6 Using a Graphing Utility to Find the Sum of a Geometric Sequence
  2254. Solution
  2255. Determine Whether a Geometric Series Converges or Diverges
  2256. Intuitive Proof
  2257. Example 7 Determining Whether a Geometric Series Converges or Diverges
  2258. Solution
  2259. Example 8 Repeating Decimals
  2260. Solution
  2261. Example 9 Pendulum Swings
  2262. Solution
  2263. 12.3 Assess Your Understanding
  2264. Concepts and Vocabulary
  2265. Skill Building
  2266. Applications and Extensions
  2267. Explaining Concepts: Discussion and Writing
  2268. 12.4 Mathematical Induction
  2269. Objective
  2270. Prove Statements Using Mathematical Induction
  2271. Example 1 Using Mathematical Induction
  2272. Solution
  2273. Example 2 Using Mathematical Induction
  2274. Solution
  2275. Example 3 Using Mathematical Induction
  2276. Solution
  2277. Example 4 Using Mathematical Induction
  2278. Solution
  2279. 12.4 Assess Your Understanding
  2280. Skill Building
  2281. Applications and Extensions
  2282. Explaining Concepts: Discussion and Writing
  2283. 12.5 The Binomial Theorem
  2284. Objectives
  2285. Evaluate (nj)
  2286. Example 1 Evaluating (nj)
  2287. Solution
  2288. Proof
  2289. Use the Binomial Theorem
  2290. Theorem Binomial Theorem
  2291. Example 2 Expanding a Binomial
  2292. Solution
  2293. Example 3 Expanding a Binomial
  2294. Solution
  2295. Example 4 Finding a Particular Coefficient in a Binomial Expansion
  2296. Solution
  2297. Example 5 Finding a Particular Term in a Binomial Expansion
  2298. Solution A
  2299. Solution B
  2300. Proof
  2301. 12.5 Assess Your Understanding
  2302. Concepts and Vocabulary
  2303. Skill Building
  2304. Applications and Extensions
  2305. Chapter Review
  2306. Things to Know
  2307. Objectives
  2308. Review Exercises
  2309. Chapter Test
  2310. Cumulative Review
  2311. Chapter Projects
  2312. 13 Counting and Probability
  2313. Outline
  2314. A Look Back
  2315. A Look Ahead
  2316. 13.1 Counting
  2317. Preparing for This Section
  2318. Objectives
  2319. 1 Find All the Subsets of a Set
  2320. Example 1 Finding All the Subsets of a Set
  2321. Solution
  2322. 2 Count the Number of Elements in a Set
  2323. Example 2 Analyzing Survey Data
  2324. Solution
  2325. Example 3 Counting
  2326. Solution
  2327. 3 Solve Counting Problems Using the Multiplication Principle
  2328. Example 4 Counting the Number of Possible Meals
  2329. Solution
  2330. Example 5 Forming Codes
  2331. Solution
  2332. 13.1 Assess Your Understanding
  2333. Concepts and Vocabulary
  2334. Skill Building
  2335. Applications and Extensions
  2336. Explaining Concepts: Discussion and Writing
  2337. Retain Your Knowledge
  2338. 13.2 Permutations and Combinations
  2339. Preparing for This Section
  2340. Objectives
  2341. 1 Solve Counting Problems Using Permutations Involving n Distinct Objects
  2342. Example 1 Counting Airport Codes [Permutation: Distinct, with Repetition]
  2343. Solution
  2344. Example 2 Forming Codes [Permutation: Distinct, without Repetition]
  2345. Solution
  2346. Example 3 Lining People Up
  2347. Solution
  2348. Example 4 Computing Permutations
  2349. Solution
  2350. Example 5 The Birthday Problem
  2351. Solution
  2352. 2 Solve Counting Problems Using Combinations
  2353. Example 6 Listing Combinations
  2354. Solution
  2355. Example 7 Using Formula (2)
  2356. Solution
  2357. Example 8 Forming Committees
  2358. Solution
  2359. Example 9 Forming Committees
  2360. Solution
  2361. 3 Solve Counting Problems Using Permutations Involving n Nondistinct Objects
  2362. Example 10 Forming Different Words
  2363. Solution
  2364. Example 11 Arranging Flags
  2365. Solution
  2366. 13.2 Assess Your Understanding
  2367. Concepts and Vocabulary
  2368. Skill Building
  2369. Applications and Extensions
  2370. Explaining Concepts: Discussion and Writing
  2371. Retain Your Knowledge
  2372. 13.3 Probability
  2373. Objectives
  2374. Example 1 Tossing a Fair Coin
  2375. 1 Construct Probability Models
  2376. Example 2 Determining Probability Models
  2377. Solution
  2378. Example 3 Constructing a Probability Model
  2379. Solution
  2380. Example 4 Constructing a Probability Model
  2381. Solution
  2382. 2 Compute Probabilities of Equally Likely Outcomes
  2383. Example 5 Calculating Probabilities of Events Involving Equally Likely Outcomes
  2384. Solution
  2385. Example 6 Computing Compound Probabilities
  2386. Solution
  2387. 3 Find Probabilities of the Union of Two Events
  2388. Example 7 Computing Probabilities of the Union of Two Events
  2389. Solution
  2390. Example 8 Computing Probabilities of the Union of Two Mutually Exclusive Events
  2391. Solution
  2392. 4 Use the Complement Rule to Find Probabilities
  2393. Example 9 Computing Probabilities Using Complements
  2394. Solution
  2395. Example 10 Birthday Problem
  2396. Solution
  2397. 13.3 Assess Your Understanding
  2398. Concepts and Vocabulary
  2399. Skill Building
  2400. Retain Your Knowledge
  2401. Chapter Review
  2402. Things to Know
  2403. Objectives
  2404. Review Exercises
  2405. Chapter Test
  2406. Chapter Test Prep Videos
  2407. Cumulative Review
  2408. Chapter Projects
  2409. 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function
  2410. Outline
  2411. A Look Back
  2412. A Look Ahead
  2413. 14.1 Finding Limits Using Tables and Graphs
  2414. Preparing for this Section
  2415. Objectives
  2416. Find a Limit Using a Table
  2417. Example 1 Finding a Limit Using a Table
  2418. Solution
  2419. Example 2 Finding a Limit Using a Table
  2420. Solution
  2421. Example 3 Finding a Limit Using a Table
  2422. Solution
  2423. Find a Limit Using a Graph
  2424. Example 4 Finding a Limit by Graphing
  2425. Solution
  2426. Example 5 A Function That Has No Limit at 0
  2427. Solution
  2428. Example 6 Using a Graphing Utility to Find a Limit
  2429. Solution
  2430. 14.1 Assess Your Understanding
  2431. Concepts and Vocabulary
  2432. Skill Building
  2433. 14.2 Algebra Techniques for Finding Limits
  2434. Objectives
  2435. Example 1 Using Formulas (1) and (2)
  2436. Find the Limit of a Sum, a Difference, and a Product
  2437. Example 2 Finding the Limit of a Sum
  2438. Solution
  2439. Example 3 Finding the Limit of a Difference
  2440. Solution
  2441. Example 4 Finding the Limit of a Product
  2442. Solution
  2443. Example 5 Finding Limits Using Algebraic Properties
  2444. Solution
  2445. Example 6 Finding the Limit of a Monomial
  2446. Solution
  2447. Find the Limit of a Polynomial
  2448. Example 7 Finding the Limit of a Polynomial
  2449. Solution
  2450. Find the Limit of a Power or a Root
  2451. Example 8 Finding the Limit of a Power or a Root
  2452. Solution
  2453. Find the Limit of a Quotient
  2454. Example 9 Finding the Limit of a Quotient
  2455. Solution
  2456. Example 10 Finding the Limit of a Quotient
  2457. Solution
  2458. Example 11 Finding Limits Using Algebraic Properties
  2459. Solution
  2460. Find the Limit of an Average Rate of Change
  2461. Example 12 Finding the Limit of an Average Rate of Change
  2462. Solution
  2463. 14.2 Assess Your Understanding
  2464. Concepts and Vocabulary
  2465. Skill Building
  2466. 14.3 One-sided Limits; Continuous Functions
  2467. Preparing for this Section
  2468. Objectives
  2469. Find the One-sided Limits of a Function
  2470. Example 1 Finding One-sided Limits of a Function
  2471. Solution
  2472. Determine Whether a Function Is Continuous
  2473. Example 2 Determining the Numbers at Which a Rational Function Is Continuous
  2474. Solution
  2475. Example 3 Determining Where a Piecewise-defined Function Is Continuous
  2476. Solution
  2477. 14.3 Assess Your Understanding
  2478. Concepts and Vocabulary
  2479. Skill Building
  2480. Explaining Concepts: Discussion and Writing
  2481. 14.4 The Tangent Problem; The Derivative
  2482. Preparing For This Section
  2483. Objectives
  2484. The Tangent Problem
  2485. Find an Equation of the Tangent Line to the Graph of a Function
  2486. Example 1 Finding an Equation of the Tangent Line
  2487. Solution
  2488. Find the Derivative of a Function
  2489. Example 2 Finding the Derivative of a Function
  2490. Solution
  2491. Example 3 Finding the Derivative of a Function Using a Graphing Utility
  2492. Solution
  2493. Example 4 Finding the Derivative of a Function
  2494. Solution
  2495. Find Instantaneous Rates of Change
  2496. Example 5 Finding the Instantaneous Rate of Change
  2497. Solution
  2498. Find the Instantaneous Velocity of a Particle
  2499. Example 6 Finding the Instantaneous Velocity of a Particle
  2500. Solution
  2501. 14.4 Assess Your Understanding
  2502. Concepts and Vocabulary
  2503. Skill Building
  2504. Applications and Extensions
  2505. 14.5 The Area Problem; The Integral
  2506. Preparing For This Section
  2507. Objectives
  2508. The Area Problem
  2509. Approximate the Area under the Graph of a Function
  2510. Example 1 Approximating the Area under the Graph of f(x) = 2x from 0 to 1
  2511. Solution
  2512. Example 2 Approximating the Area under the Graph of f(x) = x2
  2513. Solution
  2514. Definition of Area
  2515. Approximate Integrals Using a Graphing Utility
  2516. Example 3 Using a Graphing Utility to Approximate an Integral
  2517. Solution
  2518. 14.5 Assess Your Understanding
  2519. Concepts and Vocabulary
  2520. Skill Building
  2521. Chapter Review
  2522. Things to Know
  2523. Objectives
  2524. Review Exercises
  2525. Chapter Test
  2526. Chapter Projects
  2527. A Review
  2528. B The Limit of a Sequence; Infinite Series
  2529. Answers
  2530. Credits
  2531. Subject Index
  2532. LIBRARY OF FUNCTIONS

 

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