Can you do no 6 4. f(x) = eªx (−ï < x < ï), where a ‡ 0.Suggestion: Use Euler's formula eie=Answer:After evaluating this single integral, equate real parts and then imaginary parts.sinh an 2 sinh an+ΣапTAnswer:an + ibn5. f(x) = cosh ax (-л < x < л), where asinhanапAnswer:0.Suggestion: Use the series found in Problem 4.Tπ=- 1/2 [ + f(x) e¹/x dxSJ一元∞n=112a²1+2a3 ΣΣ -n=1+8cos+ i sin 0, where i = √-1, to write(-1)"a²+ n²6. f(x) = cos ax (-л < x <л), where a 0, ±1, ±2, ... .Suggestion: With the aid of Euler's formula, stated in the suggestion withProblem 4, writecos ax =(-1)"a²+ n²eiax +e2Then use the series already obtained in that earlier problem.2a sin an(-1)"+1n² - a²n=1(a cos nx n sin nx).-Cos nx-iax(n = 1, 2, ...).Cos nx

Answered: Image /qna-images/answer/db4b1222-5e39-4b19-ab18-2ac8e62effd8.jpg

4. f(x) = eªx (−ï < x < ï), where a ‡ 0. Suggestion: Use Euler's formula eie = Answer: Answer: an + ibn: 5. f(x) = cosh ax (-л < x < л), where a After evaluating this single integral, equate real parts and then imaginary parts. sinh an 2 sinh an + ап TT sinhan ал Answer: - T 0. Suggestion: Use the series found in Problem 4. 8 Σ n=1 1+2a3 Σ Σ - n=1 1 2q² = S 一元 + 8 cos+ i sin 0, where i = √-1, to write [ f(x) einx dx cos ax = (-1)" a²+ n² 6. f(x) = cos ax (-л < x <л), where a 0, ±1, ±2,.... Suggestion: With the aid of Euler's formula, stated in the suggestion with Problem 4, write n=1 (-1)" a²+ n² eiax +e 2 Then use the series already obtained in that earlier problem. 2a sin an (-1)"+1 n² - a² (a cos nx n sin nx). - Cos nx -iax (n = 1, 2, ...). Cos nx

4. f(x) = eªx (−ï < x < ï), where a ‡ 0. Suggestion: Use Euler's formula eie = Answer: Answer: an + ibn: 5. f(x) = cosh ax (-л < x < л), where a After evaluating this single integral, equate real parts and then imaginary parts. sinh an 2 sinh an + ап TT sinhan ал Answer: - T 0. Suggestion: Use the series found in Problem 4. 8 Σ n=1 1+2a3 Σ Σ - n=1 1 2q² = S 一元 + 8 cos+ i sin 0, where i = √-1, to write [ f(x) einx dx cos ax = (-1)" a²+ n² 6. f(x) = cos ax (-л < x <л), where a 0, ±1, ±2,.... Suggestion: With the aid of Euler's formula, stated in the suggestion with Problem 4, write n=1 (-1)" a²+ n² eiax +e 2 Then use the series already obtained in that earlier problem. 2a sin an (-1)"+1 n² - a² (a cos nx n sin nx). - Cos nx -iax (n = 1, 2, ...). Cos nx

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 29EQ

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