Homework Help is Here – Start Your Trial Now!
Math
Calculus
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)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 71E
See similar textbooks
icon
Related questions
Question
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)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS