By James Stewart
Stewart's MULTIVARIABLE CALCULUS: strategies AND CONTEXTS, 3rd variation bargains a streamlined method of instructing calculus, concentrating on significant thoughts and aiding people with unique definitions, sufferer factors, and punctiliously graded difficulties. MULTIVARIABLE CALCULUS: strategies AND CONTEXTS is very appeared since it has effectively introduced peace to departments that have been break up among reform and conventional ways to instructing calculus. not just does the textual content support reconcile the 2 faculties of idea via skillfully merging the easiest of conventional calculus with the easiest of the reform stream, it does so with innovation and meticulous accuracy.
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Extra resources for Multivariable Calculus: Concepts and Contexts (with Tools for Enriching Calculus, Interactive Video Skillbuilder CD-ROM, and iLrn Homework Personal Tutor)
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3n ϩ 1 (a) Determine whether ͕a n ͖ is convergent. (b) Determine whether ϱn1 a n is convergent. ͚ 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.
1 ϩ ϱ i 12. i2 ϱ bn is known to be convergent. 13. (a) If a n Ͼ bn for all n, what can you say about a n? Why? (b) If a n Ͻ bn for all n, what can you say about a n? Why? 15. ϱ 17. ͚ n1 ϱ 19. 5. It is important to distinguish between ͚ n1 ϱ ϱ ͚ n1 ͚ n2 (a) If a n Ͼ bn for all n, what can you say about an ? Why? (b) If a n Ͻ bn for all n, what can you say about an ? Why? ͚ 21. bn ͚ n1 n1 ϱ What name is given to the first series? To the second? For what values of b does the first series converge?
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 , . } ■ 1ϩ ; 29–34 this sequence appear to have a limit? If so, find it. If not, explain why. 5. ͩ ͪ 2 n n sin 2n 1 ϩ sn (b) What is a divergent sequence? Give two examples. 3. List the first six terms of the sequence defined by 22.