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34. In calculus you learned that e", cos u, and sin u can be represented by the infinite series and e" = 1+ + n! 1! n=0 u2 + 2! 3! un + + n! cos u = n=0 ∞ Σ(-1)" 1 u2n (2n)! u¹ + + 21 4! u2n +(-1)". (2n)! sin u = (-1)". n=0 u2n+1 (2n+1)! u2n+1 = U + 3! +(-1)". + 5! (2n+1)! for all real values of u. Even though you have previously considered (A) only for real values of u, we can set u = i0, where 0 is real, to obtain eio (10)" n! Given the proper background in the theory of infinite series with complex terms, it can be shown that the series in (D) converges for all real 0. (A) (B) (C) (D)

34. In calculus you learned that e", cos u, and sin u can be represented by the infinite series and e" = 1+ + n! 1! n=0 u2 + 2! 3! un + + n! cos u = n=0 ∞ Σ(-1)" 1 u2n (2n)! u¹ + + 21 4! u2n +(-1)". (2n)! sin u = (-1)". n=0 u2n+1 (2n+1)! u2n+1 = U + 3! +(-1)". + 5! (2n+1)! for all real values of u. Even though you have previously considered (A) only for real values of u, we can set u = i0, where 0 is real, to obtain eio (10)" n! Given the proper background in the theory of infinite series with complex terms, it can be shown that the series in (D) converges for all real 0. (A) (B) (C) (D)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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34. In calculus you learned that e", cos u, and sin u can be represented by the infinite series and e" = 1+ + n! 1! n=0 u2 + 2! 3! un + + n! cos u = n=0 ∞ Σ(-1)" 1 u2n (2n)! u¹ + + 21 4! u2n +(-1)". (2n)! sin u = (-1)". n=0 u2n+1 (2n+1)! u2n+1 = U + 3! +(-1)". + 5! (2n+1)! for all real values of u. Even though you have previously considered (A) only for real values of u, we can set u = i0, where 0 is real, to obtain eio (10)" n! Given the proper background in the theory of infinite series with complex terms, it can be shown that the series in (D) converges for all real 0. (A) (B) (C) (D)
Transcribed Image Text:34. In calculus you learned that e", cos u, and sin u can be represented by the infinite series and e" = 1+ + n! 1! n=0 u2 + 2! 3! un + + n! cos u = n=0 ∞ Σ(-1)" 1 u2n (2n)! u¹ + + 21 4! u2n +(-1)". (2n)! sin u = (-1)". n=0 u2n+1 (2n+1)! u2n+1 = U + 3! +(-1)". + 5! (2n+1)! for all real values of u. Even though you have previously considered (A) only for real values of u, we can set u = i0, where 0 is real, to obtain eio (10)" n! Given the proper background in the theory of infinite series with complex terms, it can be shown that the series in (D) converges for all real 0. (A) (B) (C) (D)
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