By James Stewart

Stewart's MULTIVARIABLE CALCULUS: innovations AND CONTEXTS, 3rd variation deals a streamlined method of instructing calculus, targeting significant suggestions and assisting people with particular definitions, sufferer reasons, and punctiliously graded difficulties. MULTIVARIABLE CALCULUS: innovations AND CONTEXTS is very appeared since it has effectively introduced peace to departments that have been break up among reform and conventional ways to educating calculus. not just does the textual content support reconcile the 2 faculties of idea by way of skillfully merging the easiest of conventional calculus with the easiest of the reform move, it does so with innovation and meticulous accuracy.

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**Extra info for Multivariable Calculus: Concepts and Contexts (with Tools for Enriching Calculus, Interactive Video Skillbuilder CD-ROM, and iLrn Homework Personal Tutor) **

**Sample text**

5( ) ■ 31–34 ϱ 2 n Ϫ1 28. 3 n͑n ϩ 3͒ 30. 2 ■ n1 ■ n ͚ ln n ϩ 1 n1 ■ ■ ■ ■ ■ ■ ■ ■ ■ Express the number as a ratio of integers. 32. 73737373 . . 33. 417417417 . . ■ 2 n ϩ 4n ϩ 3 2 ϱ 31. 2222 . . ■ ͚ ■ ■ ■ ■ 34. 2545454 . . 2 SERIES 35–37 (b) Calculate the total time that the ball travels. (c) Suppose that each time the ball strikes the surface with velocity v it rebounds with velocity Ϫk v, where 0 Ͻ k Ͻ 1. How long will it take for the ball to come to rest? Find the values of x for which the series converges.

N1 ϱ 9. Let a n ■ ϱ ͚ n1 ■ 1 ͚ (s2 ) n0 k2 2 k Ϫ1 k2 ■ ͑Ϫ6͒ nϪ1 5 nϪ1 ϱ 18. ϱ 1 n͑n Ϫ 1͒ ͚ 8. ■ n1 1 2n ͚ n1 n1 ϱ ■ ͚ 17–26 Determine whether the series is convergent or divergent. If it is convergent, find its sum. 6͒ 6. 16. ͚ n0 ϱ ͚ tan n n1 n 3 nϩ1 ϱ ; 3–8 12 ͑Ϫ5͒n 14. 2 nϪ1 3 n1 2. Explain what it means to say that ϱn1 a n 5. ϱ ϱ ͚ 5( ) ■ 31–34 ϱ 2 n Ϫ1 28. 3 n͑n ϩ 3͒ 30. 2 ■ n1 ■ n ͚ ln n ϩ 1 n1 ■ ■ ■ ■ ■ ■ ■ ■ ■ Express the number as a ratio of integers. 32. 73737373 .

E n ϩ e Ϫn e 2n Ϫ 1 19. ͕n 2e Ϫn ͖ nϩ1 3n Ϫ 1 sn 12. a n 1 ϩ sn ͑Ϫ1͒ nϪ1n 15. a n 2 n ϩ1 17. 10. a n ͮ 14. a n n 1 ϩ sn ͑Ϫ1͒ n n 3 16. a n 3 n ϩ 2n2 ϩ 1 18. a n cos͑2͞n͒ 20. ͕arctan 2n͖ ■ 29. a n ͑Ϫ1͒n {Ϫ 14 , 29 , Ϫ 163 , 254 , . } 8. ͕5, 1, 5, 1, 5, 1, . ͖ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. ) 5–8 {1, Ϫ 23 , 49 , Ϫ 278 , .