Test Bank for Calculus Early Transcendentals: Briggs Cochran

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  • ISBN-10 ‏ : ‎ 0134763645
  • ISBN-13 ‏ : ‎ 978-0134763644
  • Author:  Briggs Cochran

NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of the MyLab™ and Mastering™ platforms exist for each title, and registrations are not transferable. To register for and use MyLab or Mastering, you may also need a Course ID, which your instructor will provide.   Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the MyLab or Mastering platform may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. Available for fall 2020 classes The DIGITAL UPDATE gives you revised content and resources that keep your course current  For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics. This package includes 18-week access card for MyLab Math. The most successful new calculus text in the last two decades The much-anticipated 3rd Edition of Briggs’ Calculus: Early Transcendentals retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor. Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eBook contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts. For the 3rd Edition, the authors synthesized feedback on the text and MyLab™ Math content from over 140 instructors. This thorough and extensive review process, paired with the authors’ own teaching experiences, helped create a text that is designed for today’s calculus instructors and students. Personalize learning with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. 0136207685 / 9780136207689  CALCULUS, EARLY TRANSCENDENTALS PLUS MYLAB MATH WITH PEARSON ETEXT – 18-WEEK ACCESS CARD PACKAGE, 3/e

 

Table of Content:

  1. Chapter 1
  2. Chapter 3
  3. Chapter 4
  4. Chapter 5
  5. Chapter 6
  6. Chapter 7
  7. Chapter 8
  8. Chapter 10
  9. Chapter 12
  10. Chapter 13
  11. Chapter 15
  12. Chapter 16
  13. 1 Functions
  14. Chapter Preview
  15. 1.1 Review of Functions
  16. Quick Check 1
  17. Solution
  18. Solution
  19. Solution
  20. Quick Check 2
  21. Composite Functions
  22. Solution
  23. Solution
  24. Solution
  25. Solution
  26. Solution
  27. Quick Check 3
  28. Secant Lines and the Difference Quotient
  29. Solution
  30. Solution
  31. Quick Check 4
  32. Symmetry
  33. Quick Check 5
  34. Solution
  35. Section 1.1 Exercises
  36. Getting Started
  37. Practice Exercises
  38. Explorations and Challenges
  39. Quick Check Answers
  40. 1.2 Representing Functions
  41. Using Formulas
  42. Quick Check 1
  43. Using Graphs
  44. Linear Functions
  45. Solution
  46. Solution
  47. Piecewise Functions
  48. Solution
  49. Solution
  50. Power Functions
  51. Quick Check 2
  52. Root Functions
  53. Rational Functions
  54. Quick Check 3
  55. Solution
  56. Using Tables
  57. Using Words
  58. Solution
  59. Solution
  60. Transformations of Functions and Graphs
  61. Solution
  62. Quick Check 4
  63. Solution
  64. Section 1.2 Exercises
  65. Getting Started
  66. Practice Exercises
  67. Explorations and Challenges
  68. Quick Check Answers
  69. 1.3 Inverse, Exponential, and Logarithmic Functions
  70. Exponential Functions
  71. Properties of Exponential Functions
  72. Quick Check 1
  73. Quick Check 2
  74. The Natural Exponential Function
  75. Inverse Functions
  76. Quick Check 3
  77. One-to-One Functions
  78. Solution
  79. Existence of Inverse Functions
  80. Quick Check 4
  81. Solution
  82. Finding Inverse Functions
  83. Solution
  84. Quick Check 5
  85. Graphing Inverse Functions
  86. Solution
  87. Logarithmic Functions
  88. Properties of Logarithmic Functions
  89. Quick Check 6
  90. Solution
  91. Change of Base
  92. Solution
  93. Section 1.3 Exercises
  94. Getting Started
  95. Practice Exercises
  96. Explorations and Challenges
  97. Quick Check Answers
  98. 1.4 Trigonometric Functions and Their Inverses
  99. Radian Measure
  100. Quick Check 1
  101. Trigonometric Functions
  102. Solution
  103. Quick Check 2
  104. Trigonometric Identities
  105. Reciprocal Identities
  106. Pythagorean Identities
  107. Double- and Half-Angle Identities
  108. Quick Check 3
  109. Solution
  110. Graphs of the Trigonometric Functions
  111. Transforming Graphs
  112. Inverse Trigonometric Functions
  113. Inverse Sine and Cosine
  114. Quick Check 4
  115. Solution
  116. Graphs and Properties
  117. Solution
  118. Solution
  119. Other Inverse Trigonometric Functions
  120. Solution
  121. Quick Check 5
  122. Section 1.4 Exercises
  123. Getting Started
  124. Practice Exercises
  125. Explorations and Challenges
  126. Quick Check Answers
  127. Chapter 1 Review Exercises
  128. Chapter 1 Guided Projects
  129. 2 Limits
  130. Chapter Preview
  131. 2.1 The Idea of Limits
  132. Average Velocity
  133. Solution
  134. Quick Check 1
  135. Instantaneous Velocity
  136. Quick Check 2
  137. Solution
  138. Slope of the Tangent Line
  139. Quick Check 3
  140. Section 2.1 Exercises
  141. Getting Started
  142. Practice Exercises
  143. Explorations and Challenges
  144. Quick Check Answers
  145. 2.2 Definitions of Limits
  146. Solution
  147. Quick Check 1
  148. Solution
  149. One-Sided Limits
  150. Solution
  151. Solution
  152. Solution
  153. Quick Check 2
  154. Section 2.2 Exercises
  155. Getting Started
  156. Practice Exercises
  157. Explorations and Challenges
  158. Quick Check Answers
  159. 2.3 Techniques for Computing Limits
  160. Limits of Linear Functions
  161. Solution
  162. Limit Laws
  163. Solution
  164. Limits of Polynomial and Rational Functions
  165. Quick Check 1
  166. Solution
  167. Quick Check 2
  168. Solution
  169. One-Sided Limits
  170. Solution
  171. Other Techniques
  172. Solution
  173. Quick Check 3
  174. Solution
  175. An Important Limit
  176. Solution
  177. The Squeeze Theorem
  178. Solution
  179. Quick Check 4
  180. Trigonometric Limits
  181. Solution
  182. Section 2.3 Exercises
  183. Getting Started
  184. Practice Exercises
  185. Explorations and Challenges
  186. Quick Check Answers
  187. 2.4 Infinite Limits
  188. An Overview
  189. Infinite Limits
  190. Solution
  191. Quick Check 1
  192. Solution
  193. Finding Infinite Limits Analytically
  194. Solution
  195. Quick Check 2
  196. Solution
  197. Quick Check 3
  198. Solution
  199. Quick Check 4
  200. Solution
  201. Section 2.4 Exercises
  202. Getting Started
  203. Practice Exercises
  204. Explorations and Challenges
  205. Quick Check Answers
  206. 2.5 Limits at Infinity
  207. Limits at Infinity and Horizontal Asymptotes
  208. Solution
  209. Quick Check 1
  210. Infinite Limits at Infinity
  211. Quick Check 2
  212. Solution
  213. End Behavior
  214. Solution
  215. Solution
  216. Quick Check 3
  217. Solution
  218. End Behavior for and ln x
  219. Solution
  220. Quick Check 4
  221. Section 2.5 Exercises
  222. Getting Started
  223. Practice Exercises
  224. Explorations and Challenges
  225. Quick Check Answers
  226. 2.6 Continuity
  227. Continuity at a Point
  228. Solution
  229. Quick Check 1
  230. Solution
  231. Solution
  232. Solution
  233. Solution
  234. Continuity on an Interval
  235. Quick Check 2
  236. Solution
  237. Functions Involving Roots
  238. Solution
  239. Quick Check 3
  240. Continuity of Transcendental Functions
  241. Trigonometric Functions
  242. Exponential Functions
  243. Inverse Functions
  244. Solution
  245. Quick Check 4
  246. Intermediate Value Theorem
  247. Solution
  248. Quick Check 5
  249. Section 2.6 Exercises
  250. Getting Started
  251. Practice Exercises
  252. Explorations and Challenges
  253. Quick Check Answers
  254. 2.7 Precise Definitions of Limits
  255. Moving Toward a Precise Definition
  256. Solution
  257. Quick Check 1
  258. A Precise Definition
  259. Solution
  260. Quick Check 2
  261. Solution
  262. Limit Proofs
  263. Solution
  264. Solution
  265. Justifying Limit Laws
  266. Solution
  267. Infinite Limits
  268. Solution
  269. Quick Check 3
  270. Limits at Infinity
  271. Section 2.7 Exercises
  272. Getting Started
  273. Practice Exercises
  274. Explorations and Challenges
  275. Quick Check Answers
  276. Chapter 2 Review Exercises
  277. Chapter 2 Guided Projects
  278. 3 Derivatives
  279. Chapter Preview
  280. 3.1 Introducing the Derivative
  281. Solution
  282. Quick Check 1
  283. Tangent Lines and Rates of Change
  284. Quick Check 2
  285. Solution
  286. Solution
  287. Quick Check 3
  288. The Derivative
  289. Solution
  290. Quick Check 4
  291. Interpreting the Derivative
  292. Solution
  293. Solution
  294. Section 3.1 Exercises
  295. Getting Started
  296. Practice Exercises
  297. Explorations and Challenges
  298. Quick Check Answers
  299. 3.2 The Derivative as a Function
  300. The Derivative Function
  301. Solution
  302. Quick Check 1
  303. Derivative Notation
  304. Quick Check 2
  305. Solution
  306. Quick Check 3
  307. Quick Check 4
  308. Solution
  309. Graphs of Derivatives
  310. Solution
  311. Solution
  312. Quick Check 5
  313. Solution
  314. Continuity
  315. Quick Check 6
  316. Solution
  317. Section 3.2 Exercises
  318. Getting Started
  319. Practice Exercises
  320. Explorations and Challenges
  321. Quick Check Answers
  322. 3.3 Rules of Differentiation
  323. The Constant and Power Rules for Derivatives
  324. Quick Check 1
  325. Solution
  326. Quick Check 2
  327. Constant Multiple Rule
  328. Solution
  329. Sum Rule
  330. Quick Check 3
  331. Solution
  332. The Derivative of the Natural Exponential Function
  333. Quick Check 4
  334. Slopes of Tangent Lines
  335. Solution
  336. Solution
  337. Quick Check 5
  338. Higher-Order Derivatives
  339. Solution
  340. Quick Check 6
  341. Section 3.3 Exercises
  342. Getting Started
  343. Practice Exercises
  344. Explorations and Challenges
  345. Quick Check Answers
  346. 3.4 The Product and Quotient Rules
  347. Product Rule
  348. Solution
  349. Quick Check 1
  350. Quotient Rule
  351. Solution
  352. Quick Check 2
  353. Solution
  354. Extending the Power Rule to Negative Integers
  355. Quick Check 3
  356. Solution
  357. Combining Derivative Rules
  358. Solution
  359. Section 3.4 Exercises
  360. Getting Started
  361. Practice Exercises
  362. Explorations and Challenges
  363. Quick Check Answers
  364. 3.5 Derivatives of Trigonometric Functions
  365. Two Special Limits
  366. Solution
  367. Quick Check 1
  368. Derivatives of Sine and Cosine Functions
  369. Quick Check 2
  370. Solution
  371. Derivatives of Other Trigonometric Functions
  372. Solution
  373. Quick Check 3
  374. Solution
  375. Higher-Order Trigonometric Derivatives
  376. Quick Check 4
  377. Solution
  378. Section 3.5 Exercises
  379. Getting Started
  380. Practice Exercises
  381. Explorations and Challenges
  382. Quick Check Answers
  383. 3.6 Derivatives as Rates of Change
  384. One-Dimensional Motion
  385. Quick Check 1
  386. Solution
  387. Quick Check 2
  388. Solution
  389. Quick Check 3
  390. Solution
  391. Quick Check 4
  392. Growth Models
  393. Solution
  394. Quick Check 5
  395. Economics and Business
  396. Solution
  397. Quick Check 6
  398. Solution
  399. Section 3.6 Exercises
  400. Getting Started
  401. Practice Exercises
  402. Explorations and Challenges
  403. Quick Check Answers
  404. 3.7 The Chain Rule
  405. Quick Check 1
  406. Chain Rule Formulas
  407. Quick Check 2
  408. Solution
  409. Solution
  410. Solution
  411. Solution
  412. Chain Rule for Powers
  413. Solution
  414. The Composition of Three or More Functions
  415. Solution
  416. Quick Check 3
  417. Solution
  418. Proof of the Chain Rule
  419. Section 3.7 Exercises
  420. Getting Started
  421. Practice Exercises
  422. Explorations and Challenges
  423. Quick Check Answers
  424. 3.8 Implicit Differentiation
  425. Quick Check 1
  426. Solution
  427. Solution
  428. Quick Check 2
  429. Slopes of Tangent Lines
  430. Quick Check 3
  431. Solution
  432. Solution
  433. Higher-Order Derivatives of Implicit Functions
  434. Solution
  435. Section 3.8 Exercises
  436. Getting Started
  437. Practice Exercises
  438. Explorations and Challenges
  439. Quick Check Answers
  440. 3.9 Derivatives of Logarithmic and Exponential Functions
  441. The Derivative of
  442. Quick Check 1
  443. Solution
  444. Quick Check 2
  445. The Derivative of bx
  446. Solution
  447. Solution
  448. Quick Check 3
  449. The General Power Rule
  450. Solution
  451. Solution
  452. Solution
  453. Derivatives of General Logarithmic Functions
  454. Quick Check 4
  455. Solution
  456. Quick Check 5
  457. Logarithmic Differentiation
  458. Solution
  459. Section 3.9 Exercises
  460. Getting Started
  461. Practice Exercises
  462. Explorations and Challenges
  463. Quick Check Answers
  464. 3.10 Derivatives of Inverse Trigonometric Functions
  465. Inverse Sine and Its Derivative
  466. Quick Check 1
  467. Solution
  468. Derivatives of Inverse Tangent and Secant
  469. Inverse Tangent
  470. Quick Check 2
  471. Inverse Secant
  472. Quick Check 3
  473. Solution
  474. Solution
  475. Quick Check 4
  476. Derivatives of Inverse Functions in General
  477. Solution
  478. Quick Check 5
  479. Solution
  480. Solution
  481. Section 3.10 Exercises
  482. Getting Started
  483. Practice Exercises
  484. Explorations and Challenges
  485. Quick Check Answers
  486. 3.11 Related Rates
  487. Solution
  488. Quick Check 1
  489. Solution
  490. Quick Check 2
  491. Solution
  492. Quick Check 3
  493. Solution
  494. Quick Check 4
  495. Section 3.11 Exercises
  496. Getting Started
  497. Practice Exercises
  498. Explorations and Challenges
  499. Quick Check Answers
  500. Chapter 3 Review Exercises
  501. Chapter 3 Guided Projects
  502. 4 Applications of the Derivative
  503. Chapter Preview
  504. 4.1 Maxima and Minima
  505. Absolute Maxima and Minima
  506. Quick Check 1
  507. Solution
  508. Local Maxima and Minima
  509. Solution
  510. Critical Points
  511. Solution
  512. Quick Check 2
  513. Locating Absolute Maxima and Minima
  514. Solution
  515. Solution
  516. Section 4.1 Exercises
  517. Getting Started
  518. Practice Exercises
  519. Explorations and Challenges
  520. Quick Check Answers
  521. 4.2 Mean Value Theorem
  522. Rolle’s Theorem
  523. Quick Check 1
  524. Solution
  525. Mean Value Theorem
  526. Quick Check 2
  527. Solution
  528. Solution
  529. Consequences of the Mean Value Theorem
  530. Quick Check 3
  531. Section 4.2 Exercises
  532. Getting Started
  533. Practice Exercises
  534. Explorations and Challenges
  535. Quick Check Answers
  536. 4.3 What Derivatives Tell Us
  537. Increasing and Decreasing Functions
  538. Intervals of Increase and Decrease
  539. Quick Check 1
  540. Solution
  541. Solution
  542. Identifying Local Maxima and Minima
  543. Quick Check 2
  544. First Derivative Test
  545. Solution
  546. Solution
  547. Quick Check 3
  548. Absolute Extreme Values on Any Interval
  549. Solution
  550. Concavity and Inflection Points
  551. Quick Check 4
  552. Solution
  553. Solution
  554. Second Derivative Test
  555. Quick Check 5
  556. Solution
  557. Recap of Derivative Properties
  558. Section 4.3 Exercises
  559. Getting Started
  560. Practice Exercises
  561. Explorations and Challenges
  562. Quick Check Answers
  563. 4.4 Graphing Functions
  564. Calculators and Analysis
  565. Quick Check 1
  566. Graphing Guidelines
  567. Solution
  568. Quick Check 2
  569. Solution
  570. Solution
  571. Quick Check 3
  572. Solution
  573. Solution
  574. Section 4.4 Exercises
  575. Getting Started
  576. Practice Exercises
  577. Explorations and Challenges
  578. Quick Check Answers
  579. 4.5 Optimization Problems
  580. Quick Check 1
  581. Solution
  582. Quick Check 2
  583. Solution
  584. Quick Check 3
  585. Section 4.5 Exercises
  586. Getting Started
  587. Practice Exercises
  588. Explorations and Challenges
  589. Quick Check Answers
  590. 4.6 Linear Approximation and Differentials
  591. Linear Approximation
  592. Quick Check 1
  593. Solution
  594. Quick Check 2
  595. Solution
  596. Quick Check 3
  597. Solution
  598. Quick Check 4
  599. Linear Approximation and Concavity
  600. Solution
  601. A Variation on Linear Approximation
  602. Solution
  603. Quick Check 5
  604. Differentials
  605. Solution
  606. Section 4.6 Exercises
  607. Getting Started
  608. Practice Exercises
  609. Explorations and Challenges
  610. Quick Check Answers
  611. 4.7 L’Hôpital’s Rule
  612. L’ Hôpital’s Rule for the Form 0/0
  613. Solution
  614. Quick Check 1
  615. Solution
  616. Indeterminate Form
  617. Quick Check 2
  618. Solution
  619. Related Indeterminate Forms: and
  620. Solution
  621. Quick Check 3
  622. Solution
  623. Indeterminate Forms and
  624. Quick Check 4
  625. Solution
  626. Growth Rates of Functions
  627. Quick Check 5
  628. Quick Check 6
  629. Solution
  630. Solution
  631. Pitfalls in Using l’Hôpital’s Rule
  632. Section 4.7 Exercises
  633. Getting Started
  634. Practice Exercises
  635. Explorations and Challenges
  636. Quick Check Answers
  637. 4.8 Newton’s Method
  638. Why Approximate?
  639. Deriving Newton’s Method
  640. Quick Check 1
  641. Solution
  642. Quick Check 2
  643. When Do You Stop?
  644. Solution
  645. Solution
  646. Pitfalls of Newton’s Method
  647. Solution
  648. Section 4.8 Exercises
  649. Getting Started
  650. Practice Exercises
  651. Explorations and Challenges
  652. Quick Check Answers
  653. 4.9 Antiderivatives
  654. Thinking Backward
  655. Quick Check 1
  656. Solution
  657. Quick Check 2
  658. Indefinite Integrals
  659. Solution
  660. Indefinite Integrals of Trigonometric Functions
  661. Solution
  662. Quick Check 3
  663. Solution
  664. Other Indefinite Integrals
  665. Solution
  666. Solution
  667. Introduction to Differential Equations
  668. Quick Check 4
  669. Solution
  670. Motion Problems Revisited
  671. Quick Check 5
  672. Solution
  673. Solution
  674. Section 4.9 Exercises
  675. Getting Started
  676. Practice Exercises
  677. Explorations and Challenges
  678. Quick Check Answers
  679. Chapter 4 Review Exercises
  680. Chapter 4 Guided Projects
  681. 5 Integration
  682. Chapter Preview
  683. 5.1 Approximating Areas Under Curves
  684. Area Under a Velocity Curve
  685. Quick Check 1
  686. Solution
  687. Quick Check 2
  688. Approximating Areas by Riemann Sums
  689. Quick Check 3
  690. Solution
  691. Solution
  692. Quick Check 4
  693. Solution
  694. Sigma (Summation) Notation
  695. Riemann Sums Using Sigma Notation
  696. Solution
  697. Alternative Solution
  698. Section 5.1 Exercises
  699. Getting Started
  700. Practice Exercises
  701. Explorations and Challenges
  702. Quick Check Answers
  703. 5.2 Definite Integrals
  704. Net Area
  705. Solution
  706. Quick Check 1
  707. Quick Check 2
  708. The Definite Integral
  709. Notation
  710. Evaluating Definite Integrals
  711. Quick Check 3
  712. Solution
  713. Solution
  714. Quick Check 4
  715. Solution
  716. Properties of Definite Integrals
  717. Quick Check 5
  718. Integral of a Sum
  719. Constants in Integrals
  720. Integrals Over Subintervals
  721. Integrals of Absolute Values
  722. Solution
  723. Quick Check 6
  724. Bounds on Definite Integrals
  725. Nonnegative Integrand
  726. Comparing Definite Integrals
  727. Lower and Upper Bounds
  728. Evaluating Definite Integrals Using Limits
  729. Solution
  730. Section 5.2 Exercises
  731. Getting Started
  732. Practice Exercises
  733. Explorations and Challenges
  734. Quick Check Answers
  735. 5.3 Fundamental Theorem of Calculus
  736. Area Functions
  737. Solution
  738. Quick Check 1
  739. Solution
  740. Quick Check 2
  741. Fundamental Theorem of Calculus
  742. Quick Check 3
  743. The Inverse Relationship Between Differentiation and Integration
  744. Quick Check 4
  745. Solution
  746. Solution
  747. Solution
  748. Solution
  749. Solution
  750. Section 5.3 Exercises
  751. Getting Started
  752. Practice Exercises
  753. Explorations and Challenges
  754. Quick Check Answers
  755. 5.4 Working with Integrals
  756. Integrating Even and Odd Functions
  757. Quick Check 1
  758. Solution
  759. Average Value of a Function
  760. Quick Check 2
  761. Solution
  762. Mean Value Theorem for Integrals
  763. Quick Check 3
  764. Solution
  765. Section 5.4 Exercises
  766. Getting Started
  767. Practice Exercises
  768. Explorations and Challenges
  769. Quick Check Answers
  770. 5.5 Substitution Rule
  771. Indefinite Integrals
  772. Solution
  773. Quick Check 1
  774. Solution
  775. Quick Check 2
  776. Solution
  777. Substitution 1
  778. Substitution 2
  779. General Formulas for Indefinite Integrals
  780. Quick Check 3
  781. Solution
  782. Quick Check 4
  783. Definite Integrals
  784. Solution
  785. Solution
  786. Geometry of Substitution
  787. Quick Check 5
  788. Section 5.5 Exercises
  789. Getting Started
  790. Practice Exercises
  791. Explorations and Challenges
  792. Quick Check Answers
  793. Chapter 5 Review Exercises
  794. Chapter 5 Guided Projects
  795. 6 Applications of Integration
  796. Chapter Preview
  797. 6.1 Velocity and Net Change
  798. Velocity, Position, and Displacement
  799. Quick Check 1
  800. Quick Check 2
  801. Solution
  802. Future Value of the Position Function
  803. Quick Check 3
  804. Solution
  805. Quick Check 4
  806. Solution
  807. Quick Check 5
  808. Acceleration
  809. Solution
  810. Net Change and Future Value
  811. Solution
  812. Solution
  813. Quick Check 6
  814. Section 6.1 Exercises
  815. Getting Started
  816. Practice Exercises
  817. Explorations and Challenges
  818. Quick Check Answers
  819. 6.2 Regions Between Curves
  820. Quick Check 1
  821. Solution
  822. Quick Check 2
  823. Solution
  824. Integrating with Respect to y
  825. Solution
  826. Quick Check 3
  827. Solution
  828. Quick Check 4
  829. Section 6.2 Exercises
  830. Getting Started
  831. Practice Exercises
  832. Explorations and Challenges
  833. Quick Check Answers
  834. 6.3 Volume by Slicing
  835. General Slicing Method
  836. Quick Check 1
  837. Solution
  838. Solution
  839. Quick Check 2
  840. The Disk Method
  841. Quick Check 3
  842. Solution
  843. Washer Method
  844. Quick Check 4
  845. Solution
  846. Quick Check 5
  847. Revolving about the y-Axis
  848. Solution
  849. Quick Check 6
  850. Solution
  851. Section 6.3 Exercises
  852. Getting Started
  853. Practice Exercises
  854. Explorations and Challenges
  855. Quick Check Answers
  856. 6.4 Volume by Shells
  857. Cylindrical Shells
  858. Solution
  859. Quick Check 1
  860. Solution
  861. Solution
  862. Solution
  863. Quick Check 2
  864. Restoring Order
  865. Solution
  866. Quick Check 3
  867. Section 6.4 Exercises
  868. Getting Started
  869. Practice Exercises
  870. Explorations and Challenges
  871. Quick Check Answers
  872. 6.5 Length of Curves
  873. Arc Length for y = f(x)
  874. Quick Check 1
  875. Solution
  876. Solution
  877. Solution
  878. Solution
  879. Arc Length for
  880. Quick Check 2
  881. Solution
  882. Quick Check 3
  883. Solution
  884. Section 6.5 Exercises
  885. Getting Started
  886. Practice Exercises
  887. Explorations and Challenges
  888. Quick Check Answers
  889. 6.6 Surface Area
  890. Some Preliminary Calculations
  891. Quick Check 1
  892. Quick Check 2
  893. Surface Area Formula
  894. Quick Check 3
  895. Solution
  896. Solution
  897. Solution
  898. Solution
  899. Section 6.6 Exercises
  900. Getting Started
  901. Practice Exercises
  902. Explorations and Challenges
  903. Quick Check Answers
  904. 6.7 Physical Applications
  905. Density and Mass
  906. Quick Check 1
  907. Solution
  908. Quick Check 2
  909. Work
  910. Quick Check 3
  911. Solution
  912. Quick Check 4
  913. Lifting Problems
  914. Solution
  915. Quick Check 5
  916. Quick Check 6
  917. Pumping Problems
  918. Solution
  919. Quick Check 7
  920. Solution
  921. Force and Pressure
  922. Solution
  923. Section 6.7 Exercises
  924. Getting Started
  925. Practice Exercises
  926. Explorations and Challenges
  927. Quick Check Answers
  928. Chapter 6 Review Exercises
  929. Chapter 6 Guided Projects
  930. 7 Logarithmic, Exponential, and Hyperbolic Functions
  931. Chapter Preview
  932. 7.1 Logarithmic and Exponential Functions Revisited
  933. Step 1: The Natural Logarithm
  934. Properties of the Natural Logarithm
  935. Domain, Range, and Sign
  936. Derivative
  937. Quick Check 1
  938. Graph of ln x
  939. Logarithm of a Product
  940. Logarithm of a Quotient
  941. Logarithm of a Power
  942. Integrals
  943. Solution
  944. Step 2: The Exponential Function
  945. Quick Check 2
  946. Derivatives and Integrals
  947. Quick Check 3
  948. Solution
  949. Step 3: General Logarithmic and Exponential Functions
  950. Quick Check 4
  951. Solution
  952. Step 4: General Power Rule
  953. Solution
  954. Approximating e
  955. Section 7.1 Exercises
  956. Getting Started
  957. Practice Exercises
  958. Explorations and Challenges
  959. Quick Check Answers
  960. 7.2 Exponential Models
  961. Exponential Growth
  962. Solution
  963. Quick Check 1
  964. Quick Check 2
  965. Solution
  966. Quick Check 3
  967. A Financial Model
  968. Solution
  969. Resource Consumption
  970. Solution
  971. Exponential Decay
  972. Quick Check 4
  973. Radiometric Dating
  974. Solution
  975. Pharmacokinetics
  976. Solution
  977. Section 7.2 Exercises
  978. Getting Started
  979. Practice Exercises
  980. Explorations and Challenges
  981. Quick Check Answers
  982. 7.3 Hyperbolic Functions
  983. Relationship Between Trigonometric and Hyperbolic Functions
  984. Definitions, Identities, and Graphs of the Hyperbolic Functions
  985. Solution
  986. Quick Check 1
  987. Quick Check 2
  988. Derivatives and Integrals of Hyperbolic Functions
  989. Solution
  990. Quick Check 3
  991. Solution
  992. Quick Check 4
  993. Inverse Hyperbolic Functions
  994. Solution
  995. Quick Check 5
  996. Derivatives of the Inverse Hyperbolic Functions and Related Integral Formulas
  997. Solution
  998. Solution
  999. Quick Check 6
  1000. Applications of Hyperbolic Functions
  1001. The Catenary
  1002. Solution
  1003. Velocity of a Wave
  1004. Solution
  1005. Quick Check 7
  1006. Section 7.3 Exercises
  1007. Getting Started
  1008. Practice Exercises
  1009. Explorations and Challenges
  1010. Quick Check Answers
  1011. Chapter 7 Review Exercises
  1012. Chapter 7 Guided Projects
  1013. 8 Integration Techniques
  1014. Chapter Preview
  1015. 8.1 Basic Approaches
  1016. Solution
  1017. Quick Check 1
  1018. Solution
  1019. Solution
  1020. Solution
  1021. Quick Check 2
  1022. Solution
  1023. Quick Check 3
  1024. Solution
  1025. Quick Check 4
  1026. Section 8.1 Exercises
  1027. Getting Started
  1028. Practice Exercises
  1029. Explorations and Challenges
  1030. Quick Check Answers
  1031. 8.2 Integration by Parts
  1032. Integration by Parts for Indefinite Integrals
  1033. Solution
  1034. Solution
  1035. Quick Check 1
  1036. Solution
  1037. Solution
  1038. Integration by Parts for Definite Integrals
  1039. Solution
  1040. Quick Check 2
  1041. Solution
  1042. Quick Check 3
  1043. Section 8.2 Exercises
  1044. Getting Started
  1045. Practice Exercises
  1046. Explorations and Challenges
  1047. Quick Check Answers
  1048. 8.3 Trigonometric Integrals
  1049. Integrating Powers of sin x or cos x
  1050. Solution
  1051. Quick Check 1
  1052. Integrating Products of Powers of sin x and cos x
  1053. Solution
  1054. Quick Check 2
  1055. Reduction Formulas
  1056. Solution
  1057. Integrating Products of Powers of tan x and sec x
  1058. Solution
  1059. Section 8.3 Exercises
  1060. Getting Started
  1061. Practice Exercises
  1062. Explorations and Challenges
  1063. Quick Check Answers
  1064. 8.4 Trigonometric Substitutions
  1065. Integrals Involving
  1066. Quick Check 1
  1067. Solution
  1068. Solution
  1069. Integrals Involving or
  1070. Quick Check 2
  1071. Solution
  1072. Quick Check 3
  1073. Solution
  1074. Solution
  1075. Solution
  1076. Section 8.4 Exercises
  1077. Getting Started
  1078. Practice Exercises
  1079. Explorations and Challenges
  1080. Quick Check Answers
  1081. 8.5 Partial Fractions
  1082. Method of Partial Fractions
  1083. Quick Check 1
  1084. The Key Idea
  1085. Simple Linear Factors
  1086. Quick Check 2
  1087. Solution
  1088. A Shortcut (Convenient Values)
  1089. Solution
  1090. Repeated Linear Factors
  1091. Solution
  1092. Quick Check 3
  1093. Irreducible Quadratic Factors
  1094. Solution
  1095. Solution
  1096. Long Division
  1097. Quick Check 4
  1098. Section 8.5 Exercises
  1099. Getting Started
  1100. Practice Exercises
  1101. Explorations and Challenges
  1102. Quick Check Answers
  1103. 8.6 Integration Strategies
  1104. Integration Strategies
  1105. Rewrite the integrand
  1106. Solution
  1107. Quick Check 1
  1108. Try substitution
  1109. Solution
  1110. Quick Check 2
  1111. Quick Check 3
  1112. Recognize a common pattern present in the integrand
  1113. Solution
  1114. Be persistent
  1115. Solution
  1116. Multiple techniques
  1117. Solution
  1118. Section 8.6 Exercises
  1119. Getting Started
  1120. Practice Exercises
  1121. Explorations and Challenges
  1122. Quick Check Answers
  1123. 8.7 Other Methods of Integration
  1124. Using Tables of Integrals
  1125. Solution
  1126. Solution
  1127. Solution
  1128. Quick Check 1
  1129. Symbolic Methods
  1130. Quick Check 2
  1131. Solution
  1132. Quick Check 3
  1133. Solution
  1134. Section 8.7 Exercises
  1135. Getting Started
  1136. Practice Exercises
  1137. Explorations and Challenges
  1138. Quick Check Answers
  1139. 8.8 Numerical Integration
  1140. Absolute and Relative Error
  1141. Solution
  1142. Midpoint Rule
  1143. Quick Check 1
  1144. Solution
  1145. The Trapezoid Rule
  1146. Quick Check 2
  1147. Solution
  1148. Solution
  1149. Quick Check 3
  1150. Solution
  1151. Solution
  1152. Simpson’s Rule
  1153. Solution
  1154. Quick Check 4
  1155. Solution
  1156. Quick Check 5
  1157. Errors in Numerical Integration
  1158. Quick Check 6
  1159. Section 8.8 Exercises
  1160. Getting Started
  1161. Practice Exercises
  1162. Explorations and Challenges
  1163. Quick Check Answers
  1164. 8.9 Improper Integrals
  1165. Infinite Intervals
  1166. Solution
  1167. Quick Check 1
  1168. Solution
  1169. Quick Check 2
  1170. Solution
  1171. Unbounded Integrands
  1172. Quick Check 3
  1173. Solution
  1174. Solution
  1175. Solution
  1176. The Comparison Test
  1177. Solution
  1178. Quick Check 4
  1179. Section 8.9 Exercises
  1180. Getting Started
  1181. Practice Exercises
  1182. Explorations and Challenges
  1183. Quick Check Answers
  1184. Chapter 8 Review Exercises
  1185. Chapter 8 Guided Projects
  1186. 9 Differential Equations
  1187. Chapter Preview
  1188. 9.1 Basic Ideas
  1189. Solution
  1190. Solution
  1191. Quick Check 1
  1192. Solution
  1193. Quick Check 2
  1194. Solution
  1195. Quick Check 3
  1196. Differential Equations in Action
  1197. Solution
  1198. Quick Check 4
  1199. Solution
  1200. Solution
  1201. Quick Check 5
  1202. Final Note
  1203. Section 9.1 Exercises
  1204. Getting Started
  1205. Practice Exercises
  1206. Explorations and Challenges
  1207. Quick Check Answers
  1208. 9.2 Direction Fields and Euler’s Method
  1209. Direction Fields
  1210. Solution
  1211. Quick Check 1
  1212. Solution
  1213. Quick Check 2
  1214. Solution
  1215. Quick Check 3
  1216. Euler’s Method
  1217. Solution
  1218. Quick Check 4
  1219. Final Note
  1220. Section 9.2 Exercises
  1221. Getting Started
  1222. Practice Exercises
  1223. Explorations and Challenges
  1224. Quick Check Answers
  1225. 9.3 Separable Differential Equations
  1226. Method of Solution
  1227. Quick Check 1
  1228. Solution
  1229. Quick Check 2
  1230. Solution
  1231. Quick Check 3
  1232. Solution
  1233. Quick Check 4
  1234. Logistic Equation Revisited
  1235. Solution
  1236. Section 9.3 Exercises
  1237. Getting Started
  1238. Practice Exercises
  1239. Explorations and Challenges
  1240. Quick Check Answers
  1241. 9.4 Special First-Order Linear Differential Equations
  1242. Method of Solution
  1243. Quick Check 1
  1244. Solution
  1245. Quick Check 2
  1246. Solution
  1247. Quick Check 3
  1248. Solution
  1249. Newton’s Law of Cooling
  1250. Quick Check 4
  1251. Solution
  1252. Quick Check 5
  1253. Section 9.4 Exercises
  1254. Getting Started
  1255. Practice Exercises
  1256. Explorations and Challenges
  1257. Quick Check Answers
  1258. 9.5 Modeling with Differential Equations
  1259. Population Models
  1260. Quick Check 1
  1261. Solution
  1262. Solution
  1263. Stirred Tank Reactions
  1264. Quick Check 2
  1265. Solution
  1266. Predator-Prey Models
  1267. Quick Check 3
  1268. Solution
  1269. Section 9.5 Exercises
  1270. Getting Started
  1271. Practice Exercises
  1272. Explorations and Challenges
  1273. Quick Check Answers
  1274. Chapter 9 Review Exercises
  1275. Chapter 9 Guided Projects
  1276. 10 Sequences and Infinite Series
  1277. Chapter Preview
  1278. 10.1 An Overview
  1279. Examples of Sequences
  1280. Quick Check 1
  1281. Solution
  1282. Solution
  1283. Quick Check 2
  1284. Solution
  1285. Limit of a Sequence
  1286. Solution
  1287. Solution
  1288. Solution
  1289. Infinite Series and the Sequence of Partial Sums
  1290. Solution
  1291. Quick Check 3
  1292. Quick Check 4
  1293. Solution
  1294. Quick Check 5
  1295. Summary
  1296. Section 10.1 Exercises
  1297. Getting Started
  1298. Practice Exercises
  1299. Explorations and Challenges
  1300. Quick Check Answers
  1301. 10.2 Sequences
  1302. Limit of a Sequence and Limit Laws
  1303. Solution
  1304. Terminology for Sequences
  1305. Quick Check 1
  1306. Solution
  1307. Geometric Sequences
  1308. Quick Check 2
  1309. Solution
  1310. The Squeeze Theorem
  1311. Solution
  1312. Bounded Monotonic Sequence Theorem
  1313. An Application: Recurrence Relations
  1314. Solution
  1315. Quick Check 3
  1316. Growth Rates of Sequences
  1317. Quick Check 4
  1318. Solution
  1319. Formal Definition of a Limit of a Sequence
  1320. Solution
  1321. Section 10.2 Exercises
  1322. Getting Started
  1323. Practice Exercises
  1324. Explorations and Challenges
  1325. Quick Check Answers
  1326. 10.3 Infinite Series
  1327. Quick Check 1
  1328. Geometric Sums and Series
  1329. Quick Check 2
  1330. Quick Check 3
  1331. Quick Check 4
  1332. Quick Check 5
  1333. Solution
  1334. Solution
  1335. Telescoping Series
  1336. Solution
  1337. Properties of Convergent Series
  1338. Quick Check 6
  1339. Solution
  1340. Quick Check 7
  1341. Section 10.3 Exercises
  1342. Getting Started
  1343. Practice Exercises
  1344. Explorations and Challenges
  1345. Quick Check Answers
  1346. 10.4 The Divergence and Integral Tests
  1347. The Divergence Test
  1348. Solution
  1349. Quick Check 1
  1350. The Harmonic Series
  1351. The Integral Test
  1352. Solution
  1353. The p-series
  1354. Quick Check 2
  1355. Solution
  1356. Estimating the Value of Infinite Series
  1357. Quick Check 3
  1358. Solution
  1359. Section 10.4 Exercises
  1360. Getting Started
  1361. Practice Exercises
  1362. Explorations and Challenges
  1363. Quick Check Answers
  1364. 10.5 Comparison Tests
  1365. The Comparison Test
  1366. Solution
  1367. Quick Check 1
  1368. The Limit Comparison Test
  1369. Quick Check 2
  1370. Solution
  1371. Section 10.5 Exercises
  1372. Getting Started
  1373. Practice Exercises
  1374. Explorations and Challenges
  1375. Quick Check Answers
  1376. 10.6 Alternating Series
  1377. Alternating Harmonic Series
  1378. Quick Check 1
  1379. Alternating Series Test
  1380. Quick Check 2
  1381. Solution
  1382. Remainders in Alternating Series
  1383. Solution
  1384. Quick Check 3
  1385. Absolute and Conditional Convergence
  1386. Quick Check 4
  1387. Solution
  1388. Section 10.6 Exercises
  1389. Getting Started
  1390. Practice Exercises
  1391. Explorations and Challenges
  1392. Quick Check Answers
  1393. 10.7 The Ratio and Root Tests
  1394. The Ratio Test
  1395. Solution
  1396. Quick Check 1
  1397. Quick Check 2
  1398. The Root Test
  1399. Solution
  1400. Section 10.7 Exercises
  1401. Getting Started
  1402. Practice Exercises
  1403. Explorations and Challenges
  1404. Quick Check Answers
  1405. 10.8 Choosing a Convergence Test
  1406. Series Strategies
  1407. Categorize the Series
  1408. Solution
  1409. Quick Check 1
  1410. Apply the Divergence Test
  1411. Solution
  1412. Quick Check 2
  1413. Identify Special Series
  1414. Solution
  1415. Integral, Ratio, and Root Tests
  1416. Solution
  1417. Quick Check 3
  1418. Rational Terms
  1419. Solution
  1420. Section 10.8 Exercises
  1421. Getting Started
  1422. Practice Exercises
  1423. Explorations and Challenges
  1424. Quick Check Answers
  1425. Chapter 10 Review Exercises
  1426. Chapter 10 Guided Projects
  1427. 11 Power Series
  1428. Chapter Preview
  1429. 11.1 Approximating Functions with Polynomials
  1430. What Is a Power Series?
  1431. Polynomial Approximation
  1432. Linear and Quadratic Approximation
  1433. Solution
  1434. Taylor Polynomials
  1435. Quick Check 1
  1436. Solution
  1437. Quick Check 2
  1438. Quick Check 3
  1439. Approximations with Taylor Polynomials
  1440. Solution
  1441. Quick Check 4
  1442. Solution
  1443. Quick Check 5
  1444. Remainder in a Taylor Polynomial
  1445. Estimating the Remainder
  1446. Solution
  1447. Solution
  1448. Solution
  1449. Quick Check 6
  1450. Solution
  1451. Section 11.1 Exercises
  1452. Getting Started
  1453. Practice Exercises
  1454. Explorations and Challenges
  1455. Quick Check Answers
  1456. 11.2 Properties of Power Series
  1457. Geometric Series as Power Series
  1458. Quick Check 1
  1459. Convergence of Power Series
  1460. Solution
  1461. Quick Check 2
  1462. Solution
  1463. Combining Power Series
  1464. Solution
  1465. Differentiating and Integrating Power Series
  1466. Solution
  1467. Quick Check 3
  1468. Solution
  1469. Quick Check 4
  1470. Section 11.2 Exercises
  1471. Getting Started
  1472. Practice Exercises
  1473. Explorations and Challenges
  1474. Quick Check Answers
  1475. 11.3 Taylor Series
  1476. Taylor Series for a Function
  1477. Quick Check 1
  1478. Solution
  1479. Quick Check 2
  1480. Solution
  1481. Quick Check 3
  1482. Solution
  1483. Solution
  1484. Quick Check 4
  1485. The Binomial Series
  1486. Quick Check 5
  1487. Solution
  1488. Quick Check 6
  1489. Solution
  1490. Convergence of Taylor Series
  1491. Solution
  1492. Solution
  1493. Section 11.3 Exercises
  1494. Getting Started
  1495. Practice Exercises
  1496. Explorations and Challenges
  1497. Quick Check Answers
  1498. 11.4 Working with Taylor Series
  1499. Limits by Taylor Series
  1500. Solution
  1501. Quick Check 1
  1502. Solution
  1503. Differentiating Power Series
  1504. Solution
  1505. Quick Check 2
  1506. Solution
  1507. Integrating Power Series
  1508. Solution
  1509. Representing Real Numbers
  1510. Solution
  1511. Quick Check 3
  1512. Representing Functions as Power Series
  1513. Solution
  1514. Solution
  1515. Section 11.4 Exercises
  1516. Getting Started
  1517. Practice Exercises
  1518. Explorations and Challenges
  1519. Quick Check Answers
  1520. Chapter 11 Review Exercises
  1521. Chapter 11 Guided Projects
  1522. 12 Parametric and Polar Curves
  1523. Chapter Preview
  1524. 12.1 Parametric Equations
  1525. Basic Ideas
  1526. Solution
  1527. Quick Check 1
  1528. Solution
  1529. Quick Check 2
  1530. Solution
  1531. Quick Check 3
  1532. Solution
  1533. Quick Check 4
  1534. Solution
  1535. Derivatives and Parametric Equations
  1536. Quick Check 5
  1537. Solution
  1538. Arc Length
  1539. Quick Check 6
  1540. Solution
  1541. Solution
  1542. Section 12.1 Exercises
  1543. Getting Started
  1544. Practice Exercises
  1545. Explorations and Challenges
  1546. Quick Check Answers
  1547. 12.2 Polar Coordinates
  1548. Defining Polar Coordinates
  1549. Quick Check 1
  1550. Solution
  1551. Converting Between Cartesian and Polar Coordinates
  1552. Quick Check 2
  1553. Solution
  1554. Quick Check 3
  1555. Basic Curves in Polar Coordinates
  1556. Quick Check 4
  1557. Solution
  1558. Quick Check 5
  1559. Graphing in Polar Coordinates
  1560. Solution
  1561. Cartesian-to-Polar Method
  1562. Solution
  1563. Symmetry
  1564. Quick Check 6
  1565. Solution
  1566. Solution
  1567. Solution
  1568. Using Graphing Utilities
  1569. Solution
  1570. Section 12.2 Exercises
  1571. Getting Started
  1572. Practice Exercises
  1573. Explorations and Challenges
  1574. Quick Check Answers
  1575. 12.3 Calculus in Polar Coordinates
  1576. Slopes of Tangent Lines
  1577. Quick Check 1
  1578. Solution
  1579. Solution
  1580. Quick Check 2
  1581. Area of Regions Bounded by Polar Curves
  1582. Solution
  1583. Quick Check 3
  1584. Solution
  1585. Solution
  1586. Solution
  1587. Arc Length of a Polar Curve
  1588. Quick Check 4
  1589. Solution
  1590. Section 12.3 Exercises
  1591. Getting Started
  1592. Practice Exercises
  1593. Explorations and Challenges
  1594. Quick Check Answers
  1595. 12.4 Conic Sections
  1596. Parabolas
  1597. Quick Check 1
  1598. Quick Check 2
  1599. Solution
  1600. Solution
  1601. Reflection Property
  1602. Ellipses
  1603. Quick Check 3
  1604. Solution
  1605. Solution
  1606. Hyperbolas
  1607. Solution
  1608. Quick Check 4
  1609. Eccentricity and Directrix
  1610. Quick Check 5
  1611. Solution
  1612. Polar Equations of Conic Sections
  1613. Quick Check 6
  1614. Solution
  1615. Solution
  1616. Section 12.4 Exercises
  1617. Getting Started
  1618. Practice Exercises
  1619. Explorations and Challenges
  1620. Quick Check Answers
  1621. Chapter 12 Review Exercises
  1622. Chapter 12 Guided Projects
  1623. 13 Vectors and the Geometry of Space
  1624. Chapter Preview
  1625. 13.1 Vectors in the Plane
  1626. Basic Vector Operations
  1627. Scalar Multiplication
  1628. Quick Check 1
  1629. Solution
  1630. Vector Addition and Subtraction
  1631. Quick Check 2
  1632. Quick Check 3
  1633. Solution
  1634. Vector Components
  1635. Quick Check 4
  1636. Magnitude
  1637. Solution
  1638. Vector Operations in Terms of Components
  1639. Solution
  1640. Unit Vectors
  1641. Quick Check 5
  1642. Solution
  1643. Quick Check 6
  1644. Properties of Vector Operations
  1645. Quick Check 7
  1646. Applications of Vectors
  1647. Velocity Vectors
  1648. Solution
  1649. Force Vectors
  1650. Solution
  1651. Solution
  1652. Section 13.1 Exercises
  1653. Getting Started
  1654. Practice Exercises
  1655. Explorations and Challenges
  1656. Quick Check Answers
  1657. 13.2 Vectors in Three Dimensions
  1658. The xyz-Coordinate System
  1659. Solution
  1660. Quick Check 1
  1661. Equations of Simple Planes
  1662. Quick Check 2
  1663. Solution
  1664. Distances in xyz-Space
  1665. Equation of a Sphere
  1666. Solution
  1667. Solution
  1668. Quick Check 3
  1669. Vectors in R3
  1670. Quick Check 4
  1671. Solution
  1672. Magnitude and Unit Vectors
  1673. Solution
  1674. Quick Check 5
  1675. Solution
  1676. Section 13.2 Exercises
  1677. Getting Started
  1678. Practice Exercises
  1679. Explorations and Challenges
  1680. Quick Check Answers
  1681. 13.3 Dot Products
  1682. Two Forms of the Dot Product
  1683. Quick Check 1
  1684. Solution
  1685. Quick Check 2
  1686. Solution
  1687. Properties of Dot Products
  1688. Orthogonal Projections
  1689. Quick Check 3
  1690. Solution
  1691. Applications of Dot Products
  1692. Work and Force
  1693. Solution
  1694. Parallel and Normal Forces
  1695. Solution
  1696. Section 13.3 Exercises
  1697. Getting Started
  1698. Practice Exercises
  1699. Explorations and Challenges
  1700. Quick Check Answers
  1701. 13.4 Cross Products
  1702. The Cross Product
  1703. Quick Check 1
  1704. Solution
  1705. Properties of the Cross Product
  1706. Quick Check 2
  1707. Solution
  1708. Solution
  1709. Solution
  1710. Quick Check 3
  1711. Applications of the Cross Product
  1712. Torque
  1713. Solution
  1714. Magnetic Force on a Moving Charge
  1715. Solution
  1716. Section 13.4 Exercises
  1717. Getting Started
  1718. Practice Exercises
  1719. Explorations and Challenges
  1720. Quick Check Answers
  1721. 13.5 Lines and Planes in Space
  1722. Lines in Space
  1723. Quick Check 1
  1724. Solution
  1725. Solution
  1726. Quick Check 2
  1727. Distance from a Point to a Line
  1728. Quick Check 3
  1729. Solution
  1730. Solution
  1731. Equations of Planes
  1732. Quick Check 4
  1733. Solution
  1734. Solution
  1735. Quick Check 5
  1736. Solution
  1737. Parallel and Orthogonal Planes
  1738. Quick Check 6
  1739. Solution
  1740. Solution
  1741. Section 13.5 Exercises
  1742. Getting Started
  1743. Practice Exercises
  1744. Explorations and Challenges
  1745. Quick Check Answers
  1746. 13.6 Cylinders and Quadric Surfaces
  1747. Cylinders and Traces
  1748. Quick Check 1
  1749. Solution
  1750. Quadric Surfaces
  1751. Quick Check 2
  1752. Solution
  1753. Quick Check 3
  1754. Solution
  1755. Quick Check 4
  1756. Solution
  1757. Quick Check 5
  1758. Solution
  1759. Solution
  1760. Solution
  1761. Quick Check 6
  1762. Section 13.6 Exercises
  1763. Getting Started
  1764. Practice Exercises
  1765. Explorations and Challenges
  1766. Quick Check Answers
  1767. Chapter 13 Review Exercises
  1768. Chapter 13 Guided Projects
  1769. 14 Vector-Valued Functions
  1770. Chapter Preview
  1771. 14.1 Vector-Valued Functions
  1772. Vector-Valued Functions
  1773. Curves in Space
  1774. Solution
  1775. Quick Check 1
  1776. Orientation of Curves
  1777. Solution
  1778. Solution
  1779. Solution
  1780. Limits and Continuity for Vector-Valued Functions
  1781. Solution
  1782. Quick Check 2
  1783. Section 14.1 Exercises
  1784. Getting Started
  1785. Practice Exercises
  1786. Explorations and Challenges
  1787. Quick Check Answers
  1788. 14.2 Calculus of Vector-Valued Functions
  1789. The Derivative and Tangent Vector
  1790. Solution
  1791. Quick Check 1
  1792. Unit Tangent Vector
  1793. Quick Check 2
  1794. Solution
  1795. Derivative Rules
  1796. Quick Check 3
  1797. Solution
  1798. Higher-Order Derivatives
  1799. Solution
  1800. Integrals of Vector-Valued Functions
  1801. Solution
  1802. Quick Check 4
  1803. Solution
  1804. Solution
  1805. Section 14.2 Exercises
  1806. Getting Started
  1807. Practice Exercises
  1808. Explorations and Challenges
  1809. Quick Check Answers
  1810. 14.3 Motion in Space
  1811. Position, Velocity, Speed, Acceleration
  1812. Quick Check 1
  1813. Solution
  1814. Solution
  1815. Quick Check 2
  1816. Straight-Line and Circular Motion
  1817. Solution
  1818. Quick Check 3
  1819. Two-Dimensional Motion in a Gravitational Field
  1820. Finding Velocity and Position from Acceleration
  1821. Solution
  1822. Quick Check 4
  1823. Range, Time of Flight, Maximum Height
  1824. Quick Check 5
  1825. Solution
  1826. Three-Dimensional Motion
  1827. Solution
  1828. Section 14.3 Exercises
  1829. Getting Started
  1830. Practice Exercises
  1831. Explorations and Challenges
  1832. Quick Check Answers
  1833. 14.4 Length of Curves
  1834. Arc Length
  1835. Quick Check 1
  1836. Solution
  1837. Solution
  1838. Arc Length as a Parameter
  1839. Quick Check 2
  1840. The Arc Length Function
  1841. Solution
  1842. Quick Check 3
  1843. Section 14.4 Exercises
  1844. Getting Started
  1845. Practice Exercises
  1846. Explorations and Challenges
  1847. Quick Check Answers
  1848. 14.5 Curvature and Normal Vectors
  1849. Curvature
  1850. Unit Tangent Vector
  1851. Solution
  1852. Solution
  1853. Quick Check 1
  1854. An Alternative Curvature Formula
  1855. Quick Check 2
  1856. Solution
  1857. Solution
  1858. Principal Unit Normal Vector
  1859. Quick Check 3
  1860. Solution
  1861. Quick Check 4
  1862. Components of the Acceleration
  1863. Solution
  1864. Solution
  1865. Quick Check 5
  1866. The Binormal Vector and Torsion
  1867. Quick Check 6
  1868. Quick Check 7
  1869. Solution
  1870. Solution
  1871. Section 14.5 Exercises
  1872. Getting Started
  1873. Practice Exercises
  1874. Explorations and Challenges
  1875. Quick Check Answers
  1876. Chapter 14 Review Exercises
  1877. Chapter 14 Guided Projects
  1878. 15 Functions of Several Variables
  1879. Chapter Preview
  1880. 15.1 Graphs and Level Curves
  1881. Functions of Two Variables
  1882. Solution
  1883. Quick Check 1
  1884. Graphs of Functions of Two Variables
  1885. Quick Check 2
  1886. Solution
  1887. Quick Check 3
  1888. Level Curves
  1889. Quick Check 4
  1890. Quick Check 5
  1891. Solution
  1892. Quick Check 6
  1893. Solution
  1894. Applications of Functions of Two Variables
  1895. Solution
  1896. Quick Check 7
  1897. Solution
  1898. Quick Check 8
  1899. Functions of More Than Two Variables
  1900. Solution
  1901. Quick Check 9
  1902. Graphs of Functions of More Than Two Variables
  1903. Section 15.1 Exercises
  1904. Getting Started
  1905. Practice Exercises
  1906. Explorations and Challenges
  1907. Quick Check Answers
  1908. 15.2 Limits and Continuity
  1909. Limit of a Function of Two Variables
  1910. Solution
  1911. Quick Check 1
  1912. Limits at Boundary Points
  1913. Quick Check 2
  1914. Quick Check 3
  1915. Solution
  1916. Solution
  1917. Quick Check 4
  1918. Continuity of Functions of Two Variables
  1919. Solution
  1920. Composite Functions
  1921. Quick Check 5
  1922. Solution
  1923. Functions of Three Variables
  1924. Solution
  1925. Section 15.2 Exercises
  1926. Getting Started
  1927. Practice Exercises
  1928. Explorations and Challenges
  1929. Quick Check Answers
  1930. 15.3 Partial Derivatives
  1931. Derivatives with Two Variables
  1932. Notation
  1933. Calculating Partial Derivatives
  1934. Solution
  1935. Solution
  1936. Quick Check 1
  1937. Solution
  1938. Higher-Order Partial Derivatives
  1939. Quick Check 2
  1940. Solution
  1941. Quick Check 3
  1942. Equality of Mixed Partial Derivatives
  1943. Functions of Three Variables
  1944. Solution
  1945. Quick Check 4
  1946. Applications of Partial Derivatives
  1947. Solution
  1948. Quick Check 5
  1949. Differentiability
  1950. Solution
  1951. Section 15.3 Exercises
  1952. Getting Started
  1953. Practice Exercises
  1954. Explorations and Challenges
  1955. Quick Check Answers
  1956. 15.4 The Chain Rule
  1957. The Chain Rule with One Independent Variable
  1958. Quick Check 1
  1959. Solution
  1960. The Chain Rule with Several Independent Variables
  1961. Quick Check 2
  1962. Solution
  1963. Solution
  1964. Quick Check 3
  1965. Solution
  1966. Implicit Differentiation
  1967. Solution
  1968. Quick Check 4
  1969. Solution
  1970. Solution
  1971. Section 15.4 Exercises
  1972. Getting Started
  1973. Practice Exercises
  1974. Explorations and Challenges
  1975. Quick Check Answers
  1976. 15.5 Directional Derivatives and the Gradient
  1977. Directional Derivatives
  1978. Quick Check 1
  1979. Quick Check 2
  1980. Solution
  1981. Quick Check 3
  1982. The Gradient Vector
  1983. Solution
  1984. Solution
  1985. Interpretations of the Gradient
  1986. Solution
  1987. Solution
  1988. The Gradient and Level Curves
  1989. Quick Check 4
  1990. Solution
  1991. Solution
  1992. Quick Check 5
  1993. The Gradient in Three Dimensions
  1994. Quick Check 6
  1995. Solution
  1996. Section 15.5 Exercises
  1997. Getting Started
  1998. Practice Exercises
  1999. Explorations and Challenges
  2000. Quick Check Answers
  2001. 15.6 Tangent Planes and Linear Approximation
  2002. Tangent Planes
  2003. Quick Check 1
  2004. Tangent Planes for
  2005. Solution
  2006. Tangent Planes for
  2007. Solution
  2008. Linear Approximation
  2009. Solution
  2010. Quick Check 2
  2011. Differentials and Change
  2012. Quick Check 3
  2013. Solution
  2014. Solution
  2015. Quick Check 4
  2016. Solution
  2017. Section 15.6 Exercises
  2018. Getting Started
  2019. Practice Exercises
  2020. Explorations and Challenges
  2021. Quick Check Answers
  2022. 15.7 Maximum/Minimum Problems
  2023. Local Maximum/Minimum Values
  2024. Quick Check 1
  2025. Solution
  2026. Second Derivative Test
  2027. Quick Check 2
  2028. Quick Check 3
  2029. Solution
  2030. Solution
  2031. Solution
  2032. Absolute Maximum and Minimum Values
  2033. Solution
  2034. Solution
  2035. Solution
  2036. Open and/or Unbounded Regions
  2037. Solution
  2038. Quick Check 4
  2039. Solution
  2040. Section 15.7 Exercises
  2041. Getting Started
  2042. Practice Exercises
  2043. Explorations and Challenges
  2044. Quick Check Answers
  2045. 15.8 Lagrange Multipliers
  2046. The Basic Idea
  2047. Lagrange Multipliers with Two Independent Variables
  2048. Quick Check 1
  2049. Solution
  2050. Quick Check 2
  2051. Lagrange Multipliers with Three Independent Variables
  2052. Solution
  2053. Quick Check 3
  2054. Economic Models
  2055. Solution
  2056. Quick Check 4
  2057. Section 15.8 Exercises
  2058. Getting Started
  2059. Practice Exercises
  2060. Explorations and Challenges
  2061. Quick Check Answers
  2062. Chapter 15 Review Exercises
  2063. Chapter 15 Guided Projects
  2064. 16 Multiple Integration
  2065. Chapter Preview
  2066. 16.1 Double Integrals over Rectangular Regions
  2067. Volumes of Solids
  2068. Quick Check 1
  2069. Iterated Integrals
  2070. Solution
  2071. Solution
  2072. Quick Check 2
  2073. Solution
  2074. Quick Check 3
  2075. Solution
  2076. Average Value
  2077. Solution
  2078. Section 16.1 Exercises
  2079. Getting Started
  2080. Practice Exercises
  2081. Explorations and Challenges
  2082. Quick Check Answers
  2083. 16.2 Double Integrals over General Regions
  2084. General Regions of Integration
  2085. Iterated Integrals
  2086. Solution
  2087. Quick Check 1
  2088. Change of Perspective
  2089. Solution
  2090. Quick Check 2
  2091. Choosing and Changing the Order of Integration
  2092. Solution
  2093. Solution
  2094. Quick Check 3
  2095. Regions Between Two Surfaces
  2096. Solution
  2097. Decomposition of Regions
  2098. Finding Area by Double Integrals
  2099. Solution
  2100. Quick Check 4
  2101. Section 16.2 Exercises
  2102. Getting Started
  2103. Practice Exercises
  2104. Explorations and Challenges
  2105. Quick Check Answers
  2106. 16.3 Double Integrals in Polar Coordinates
  2107. Moving from Rectangular to Polar Coordinates
  2108. Quick Check 1
  2109. Solution
  2110. Quick Check 2
  2111. Solution
  2112. Quick Check 3
  2113. Solution
  2114. More General Polar Regions
  2115. Solution
  2116. Areas of Regions
  2117. Solution
  2118. Quick Check 4
  2119. Average Value over a Planar Polar Region
  2120. Solution
  2121. Section 16.3 Exercises
  2122. Getting Started
  2123. Practice Exercises
  2124. Explorations and Challenges
  2125. Quick Check Answers
  2126. 16.4 Triple Integrals
  2127. Triple Integrals in Rectangular Coordinates
  2128. Quick Check 1
  2129. Finding Limits of Integration
  2130. Solution
  2131. Quick Check 2
  2132. Solution
  2133. Quick Check 3
  2134. Solution
  2135. Changing the Order of Integration
  2136. Solution
  2137. Average Value of a Function of Three Variables
  2138. Solution
  2139. Quick Check 4
  2140. Section 16.4 Exercises
  2141. Getting Started
  2142. Practice Exercises
  2143. Explorations and Challenges
  2144. Quick Check Answers
  2145. 16.5 Triple Integrals in Cylindrical and Spherical Coordinates
  2146. Cylindrical Coordinates
  2147. Solution
  2148. Quick Check 1
  2149. Integration in Cylindrical Coordinates
  2150. Finding Limits of Integration
  2151. Solution
  2152. Quick Check 2
  2153. Solution
  2154. Solution
  2155. Spherical Coordinates
  2156. Quick Check 3
  2157. Solution
  2158. Integration in Spherical Coordinates
  2159. Finding Limits of Integration
  2160. Solution
  2161. Solution
  2162. Section 16.5 Exercises
  2163. Getting Started
  2164. Practice Exercises
  2165. Explorations and Challenges
  2166. Quick Check Answers
  2167. 16.6 Integrals for Mass Calculations
  2168. Sets of Individual Objects
  2169. Quick Check 1
  2170. Quick Check 2
  2171. Several Objects on a Line
  2172. Solution
  2173. Continuous Objects in One Dimension
  2174. Quick Check 3
  2175. Solution
  2176. Two-Dimensional Objects
  2177. Quick Check 4
  2178. Solution
  2179. Solution
  2180. Three-Dimensional Objects
  2181. Quick Check 5
  2182. Solution
  2183. Solution
  2184. Section 16.6 Exercises
  2185. Getting Started
  2186. Practice Exercises
  2187. Explorations and Challenges
  2188. Quick Check Answers
  2189. 16.7 Change of Variables in Multiple Integrals
  2190. Recap of Change of Variables
  2191. Transformations in the Plane
  2192. Solution
  2193. Quick Check 1
  2194. Quick Check 2
  2195. Solution
  2196. Solution
  2197. Quick Check 3
  2198. Solution
  2199. Quick Check 4
  2200. Solution
  2201. Change of Variables in Triple Integrals
  2202. Solution
  2203. Quick Check 5
  2204. Strategies for Choosing New Variables
  2205. Section 16.7 Exercises
  2206. Getting Started
  2207. Practice Exercises
  2208. Explorations and Challenges
  2209. Quick Check Answers
  2210. Chapter 16 Review Exercises
  2211. Chapter 16 Guided Projects
  2212. 17 Vector Calculus
  2213. Chapter Preview
  2214. 17.1 Vector Fields
  2215. Vector Fields in Two Dimensions
  2216. Solution
  2217. Quick Check 1
  2218. Radial Vector Fields in
  2219. Solution
  2220. Quick Check 2
  2221. Vector Fields in Three Dimensions
  2222. Solution
  2223. Gradient Fields and Potential Functions
  2224. Quick Check 3
  2225. Solution
  2226. Equipotential Curves and Surfaces
  2227. Solution
  2228. Section 17.1 Exercises
  2229. Getting Started
  2230. Practice Exercises
  2231. Explorations and Challenges
  2232. Quick Check Answers
  2233. 17.2 Line Integrals
  2234. Scalar Line Integrals in the Plane
  2235. Evaluating Line Integrals
  2236. Quick Check 1
  2237. Solution
  2238. Quick Check 2
  2239. Line Integrals in
  2240. Solution
  2241. Solution
  2242. Quick Check 3
  2243. Line Integrals of Vector Fields
  2244. Solution
  2245. Work Integrals
  2246. Quick Check 4
  2247. Solution
  2248. Circulation and Flux of a Vector Field
  2249. Circulation
  2250. Solution
  2251. Solution
  2252. Flux of Two-Dimensional Vector Fields
  2253. Quick Check 5
  2254. Solution
  2255. Section 17.2 Exercises
  2256. Getting Started
  2257. Practice Exercises
  2258. Explorations and Challenges
  2259. Quick Check Answers
  2260. 17.3 Conservative Vector Fields
  2261. Types of Curves and Regions
  2262. Quick Check 1
  2263. Test for Conservative Vector Fields
  2264. Solution
  2265. Finding Potential Functions
  2266. Quick Check 2
  2267. Solution
  2268. Quick Check 3
  2269. Fundamental Theorem for Line Integrals and Path Independence
  2270. Solution
  2271. Solution
  2272. Quick Check 4
  2273. Line Integrals on Closed Curves
  2274. Solution
  2275. Summary of the Properties of Conservative Vector Fields
  2276. Section 17.3 Exercises
  2277. Getting Started
  2278. Practice Exercises
  2279. Explorations and Challenges
  2280. Quick Check Answers
  2281. 17.4 Green’s Theorem
  2282. Circulation Form of Green’s Theorem
  2283. Quick Check 1
  2284. Solution
  2285. Calculating Area by Green’s Theorem
  2286. Solution
  2287. Flux Form of Green’s Theorem
  2288. Quick Check 2
  2289. Solution
  2290. Solution
  2291. Circulation and Flux on More General Regions
  2292. Solution
  2293. Solution
  2294. Stream Functions
  2295. Quick Check 3
  2296. Proof of Green’s Theorem on Special Regions
  2297. Quick Check 4
  2298. Section 17.4 Exercises
  2299. Getting Started
  2300. Practice Exercises
  2301. Explorations and Challenges
  2302. Quick Check Answers
  2303. 17.5 Divergence and Curl
  2304. The Divergence
  2305. Solution
  2306. Quick Check 1
  2307. Divergence of a Radial Vector Field
  2308. Solution
  2309. Solution
  2310. Quick Check 2
  2311. The Curl
  2312. Curl of a General Rotation Vector Field
  2313. Quick Check 3
  2314. Solution
  2315. Working with Divergence and Curl
  2316. Quick Check 4
  2317. Solution
  2318. Summary of Properties of Conservative Vector Fields
  2319. Section 17.5 Exercises
  2320. Getting Started
  2321. Practice Exercises
  2322. Explorations and Challenges
  2323. Quick Check Answers
  2324. 17.6 Surface Integrals
  2325. Parameterized Surfaces
  2326. Cylinders
  2327. Quick Check 1
  2328. Cones
  2329. Quick Check 2
  2330. Spheres
  2331. Quick Check 3
  2332. Solution
  2333. Surface Integrals of Scalar-Valued Functions
  2334. Solution
  2335. Solution
  2336. Solution
  2337. Surface Integrals on Explicitly Defined Surfaces
  2338. Solution
  2339. Quick Check 4
  2340. Solution
  2341. Quick Check 5
  2342. Surface Integrals of Vector Fields
  2343. Flux Integrals
  2344. Solution
  2345. Solution
  2346. Quick Check 6
  2347. Section 17.6 Exercises
  2348. Getting Started
  2349. Practice Exercises
  2350. Explorations and Challenges
  2351. Quick Check Answers
  2352. 17.7 Stokes’ Theorem
  2353. Stokes’ Theorem
  2354. Quick Check 1
  2355. Solution
  2356. Solution
  2357. Solution
  2358. Quick Check 2
  2359. Interpreting the Curl
  2360. Solution
  2361. Quick Check 3
  2362. Proof of Stokes’ Theorem
  2363. Two Final Notes on Stokes’ Theorem
  2364. Section 17.7 Exercises
  2365. Getting Started
  2366. Practice Exercises
  2367. Explorations and Challenges
  2368. Quick Check Answers
  2369. 17.8 Divergence Theorem
  2370. Divergence Theorem
  2371. Quick Check 1
  2372. Solution
  2373. Solution
  2374. Solution
  2375. Quick Check 2
  2376. Interpretation of the Divergence Theorem Using Mass Transport
  2377. Quick Check 3
  2378. Proof of the Divergence Theorem
  2379. Divergence Theorem for Hollow Regions
  2380. Solution
  2381. Gauss’ Law
  2382. A Final Perspective
  2383. Section 17.8 Exercises
  2384. Getting Started
  2385. Practice Exercises
  2386. Explorations and Challenges
  2387. Quick Check Answers
  2388. Chapter 17 Review Exercises
  2389. Chapter 17 Guided Projects
  2390. A Appendix
  2391. B Appendix
  2392. Algebra
  2393. Solution
  2394. Sets of Real Numbers
  2395. Solution
  2396. Absolute Value
  2397. Solution
  2398. Cartesian Coordinate System
  2399. Distance Formula and Circles
  2400. Solution
  2401. Equations of Lines
  2402. Solution
  2403. Parallel and Perpendicular Lines
  2404. Solution
  2405. Solution
  2406. Appendix B Exercises
  2407. Getting Started
  2408. Practice Exercises
  2409. Explorations and Challenges
  2410. Answers
  2411. Appendix B
  2412. Exercises, pp. B-7–B-8
  2413. C Appendix
  2414. Complex Numbers
  2415. Complex Arithmetic
  2416. Solution
  2417. Solution
  2418. Euler’s Formula
  2419. Solution
  2420. Solution
  2421. Polar Form of Complex Numbers
  2422. Solution
  2423. Appendix C Exercises
  2424. Practice Exercises
  2425. Explorations and Challenges
  2426. Answers
  2427. Appendix C
  2428. Exercises, p. C-6
  2429. Answers
  2430. Chapter 1
  2431. Section 1.1 Exercises, pp. 9–13
  2432. Section 1.2 Exercises, pp. 22–27
  2433. Section 1.3 Exercises, pp. 35–39
  2434. Section 1.4 Exercises, pp. 48–51
  2435. Chapter 1 Review Exercises, pp. 51–55
  2436. Chapter 2
  2437. Section 2.1 Exercises, pp. 61–62
  2438. Section 2.2 Exercises, pp. 67–71
  2439. Section 2.3 Exercises, pp. 79–82
  2440. Section 2.4 Exercises, pp. 88–91
  2441. Section 2.5 Exercises, pp. 100–102
  2442. Section 2.6 Exercises, pp. 112–115
  2443. Section 2.7 Exercises, pp. 124–128
  2444. Chapter 2 Review Exercises, pp. 128–130
  2445. Chapter 3
  2446. Section 3.1 Exercises, pp. 137–140
  2447. Section 3.2 Exercises, pp. 148–152
  2448. Section 3.3 Exercises, pp. 159–162
  2449. Section 3.4 Exercises, pp. 168–170
  2450. Section 3.5 Exercises, pp. 175–178
  2451. Section 3.6 Exercises, pp. 186–191
  2452. Section 3.7 Exercises, pp. 196–200
  2453. Section 3.8 Exercises, pp. 205–208
  2454. Section 3.9 Exercises, pp. 215–218
  2455. Section 3.10 Exercises, pp. 225–227
  2456. Section 3.11 Exercises, pp. 231–236
  2457. Chapter 3 Review Exercises, pp. 236–240
  2458. Chapter 4
  2459. Section 4.1 Exercises, pp. 247–250
  2460. Section 4.2 Exercises, pp. 254–257
  2461. Section 4.3 Exercises, pp. 267–270
  2462. Section 4.4 Exercises, pp. 277–280
  2463. Section 4.5 Exercises, pp. 284–291
  2464. Section 4.6 Exercises, pp. 298–300
  2465. Section 4.7 Exercises, pp. 310–312
  2466. Section 4.8 Exercises, pp. 318–321
  2467. Section 4.9 Exercises, pp. 331–334
  2468. Chapter 4 Review Exercises, pp. 334–337
  2469. Chapter 5
  2470. Section 5.1 Exercises, pp. 347–352
  2471. Section 5.2 Exercises, pp. 364–367
  2472. Section 5.3 Exercises, pp. 377–381
  2473. Section 5.4 Exercises, pp. 385–387
  2474. Section 5.5 Exercises, pp. 395–398
  2475. Chapter 5 Review Exercises, pp. 398–402
  2476. Chapter 6
  2477. Section 6.1 Exercises, pp. 410–416
  2478. Section 6.2 Exercises, pp. 420–425
  2479. Section 6.3 Exercises, pp. 434–439
  2480. Section 6.4 Exercises, pp. 447–451
  2481. Section 6.5 Exercises, pp. 455–457
  2482. Section 6.6 Exercises, pp. 463–465
  2483. Section 6.7 Exercises, pp. 473–477
  2484. Chapter 6 Review Exercises, pp. 478–482
  2485. Chapter 7
  2486. Section 7.1 Exercises, pp. 490–492
  2487. Section 7.2 Exercises, pp. 499–501
  2488. Section 7.3 Exercises, pp. 513–517
  2489. Chapter 7 Review Exercises, pp. 518–519
  2490. Chapter 8
  2491. Section 8.1 Exercises, pp. 523–525
  2492. Section 8.2 Exercises, pp. 529–532
  2493. Section 8.3 Exercises, pp. 536–538
  2494. Section 8.4 Exercises, pp. 543–546
  2495. Section 8.5 Exercises, pp. 554–556
  2496. Section 8.6 Exercises, pp. 560–562
  2497. Section 8.7 Exercises, pp. 565–567
  2498. Section 8.8 Exercises, pp. 578–582
  2499. Section 8.9 Exercises, pp. 590–593
  2500. Chapter 8 Review Exercises, pp. 593–596
  2501. Chapter 9
  2502. Section 9.1 Exercises, pp. 604–606
  2503. Section 9.2 Exercises, pp. 611–614
  2504. Section 9.3 Exercises, pp. 618–620
  2505. Section 9.4 Exercises, pp. 625–627
  2506. Section 9.5 Exercises, pp. 634–636
  2507. Chapter 9 Review Exercises, pp. 636–638
  2508. Chapter 10
  2509. Section 10.1 Exercises, pp. 647–649
  2510. Section 10.2 Exercises, pp. 659–662
  2511. Section 10.3 Exercises, pp. 668–671
  2512. Section 10.4 Exercises, pp. 680–683
  2513. Section 10.5 Exercises, pp. 687–688
  2514. Section 10.6 Exercises, pp. 694–696
  2515. Section 10.7 Exercises, pp. 699–700
  2516. Section 10.8 Exercises, pp. 703–704
  2517. Chapter 10 Review Exercises, pp. 704–707
  2518. Chapter 11
  2519. Section 11.1 Exercises, pp. 718–721
  2520. Section 11.2 Exercises, pp. 729–730
  2521. Section 11.3 Exercises, pp. 740–742
  2522. Section 11.4 Exercises, pp. 748–750
  2523. Chapter 11 Review Exercises, pp. 750–752
  2524. Chapter 12
  2525. Section 12.1 Exercises, pp. 763–767
  2526. Section 12.2 Exercises, pp. 775 779
  2527. Section 12.3 Exercises, pp. 786–788
  2528. Section 12.4 Exercises, pp. 797–800
  2529. Chapter 12 Review Exercises, pp. 800–803
  2530. Chapter 13
  2531. Section 13.1 Exercises, pp. 813–816
  2532. Section 13.2 Exercises, pp. 823–827
  2533. Section 13.3 Exercises, pp. 833–837
  2534. Section 13.4 Exercises, pp. 842–844
  2535. Section 13.5 Exercises, pp. 852–855
  2536. Section 13.6 Exercises, pp. 863–865
  2537. Chapter 13 Review Exercises, pp. 865–867
  2538. Chapter 14
  2539. Section 14.1 Exercises, pp. 873–875
  2540. Section 14.2 Exercises, pp. 881–883
  2541. Section 14.3 Exercises, pp. 892–896
  2542. Section 14.4 Exercises, pp. 900–902
  2543. Section 14.5 Exercises, pp. 913–915
  2544. Chapter 14 Review Exercises, pp. 916–918
  2545. Chapter 15
  2546. Section 15.1 Exercises, pp. 927–930
  2547. Section 15.2 Exercises, pp. 937–939
  2548. Section 15.3 Exercises, pp. 948–951
  2549. Section 15.4 Exercises, pp. 957–961
  2550. Section 15.5 Exercises, pp. 970–973
  2551. Section 15.6 Exercises, pp. 980–983
  2552. Section 15.7 Exercises, pp. 993–996
  2553. Section 15.8 Exercises, pp. 1002–1004
  2554. Chapter 15 Review Exercises, pp. 1005–1007
  2555. Chapter 16
  2556. Section 16.1 Exercises, pp. 1015–1017
  2557. Section 16.2 Exercises, pp. 1024–1027
  2558. Section 16.3 Exercises, pp. 1033–1036
  2559. Section 16.4 Exercises, pp. 1043–1047
  2560. Section 16.5 Exercises, pp. 1059–1063
  2561. Section 16.6 Exercises, pp. 1070–1072
  2562. Section 16.7 Exercises, pp. 1082–1084
  2563. Chapter 16 Review Exercises, pp. 1084–1088
  2564. Chapter 17
  2565. Section 17.1 Exercises, pp. 1096–1098
  2566. Section 17.2 Exercises, pp. 1110–1114
  2567. Section 17.3 Exercises, pp. 1121–1123
  2568. Section 17.4 Exercises, pp. 1133–1136
  2569. Section 17.5 Exercises, pp. 1143–1146
  2570. Section 17.6 Exercises, pp. 1159–1161
  2571. Section 17.7 Exercises, pp. 1169–1171
  2572. Section 17.8 Exercises, pp. 1179–1182
  2573. Chapter 17 Review Exercises, pp. 1182–1184
  2574. Index
  2575. A
  2576. B
  2577. C
  2578. D
  2579. E
  2580. F
  2581. G
  2582. H
  2583. I
  2584. J
  2585. K
  2586. L
  2587. M
  2588. N
  2589. O
  2590. P
  2591. Q
  2592. R
  2593. S
  2594. T
  2595. U
  2596. V
  2597. W
  2598. X
  2599. Y
  2600. Z
  2601. Index of Applications
  2602. Economics and Business
  2603. Engineering and Physical Sciences
  2604. General
  2605. Life Sciences
  2606. Social and Behavioral Sciences
  2607. Table of Integrals