For the function f(z) = 24/(64 + 26): i. Find the singular points of f(z) and sketch them on the complex plane ii. Calculate the residues of the function f(z) at its singular points. iii. Hence, use the method of contour integration, the Cauchy residue Theorem and the Estimation Lemma to show that I x4 = Ĵ П dx = 64 + x6 3
For the function f(z) = 24/(64 + 26): i. Find the singular points of f(z) and sketch them on the complex plane ii. Calculate the residues of the function f(z) at its singular points. iii. Hence, use the method of contour integration, the Cauchy residue Theorem and the Estimation Lemma to show that I x4 = Ĵ П dx = 64 + x6 3
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
Question
![For the function f(z) = 24/(64 + 26):
i. Find the singular points of f(z) and sketch them on the complex plane
ii. Calculate the residues of the function f(z) at its singular points.
iii. Hence, use the method of contour integration, the Cauchy residue Theorem
and the Estimation Lemma to show that
I
x4
=
Ĵ
П
dx
=
64 + x6
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc05cf68-81ae-4970-8864-261fc4d70f9c%2F1385d9a0-e1e5-4e50-b945-acc7bb1c8761%2Fy9xc8cp_processed.png&w=3840&q=75)
Transcribed Image Text:For the function f(z) = 24/(64 + 26):
i. Find the singular points of f(z) and sketch them on the complex plane
ii. Calculate the residues of the function f(z) at its singular points.
iii. Hence, use the method of contour integration, the Cauchy residue Theorem
and the Estimation Lemma to show that
I
x4
=
Ĵ
П
dx
=
64 + x6
3
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