7. Let (2-1)²(2+3) 1-sin(72/2) f(z) = (a) Find all the singularities of f and identify each as a removable singularity, a pole (give the order), or an essential singularity. (b) Determine and classify the zeros of f.
7. Let (2-1)²(2+3) 1-sin(72/2) f(z) = (a) Find all the singularities of f and identify each as a removable singularity, a pole (give the order), or an essential singularity. (b) Determine and classify the zeros of f.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7. Let
f(x) =
(a) Find all the singularities of f and identify each as a removable singularity, a pole (give the
order), or an essential singularity.
(b) Determine and classify the zeros of f.
8. Evaluate the following integrals using the residue theorem:
x sin x
(a) Loo
(b)
(c)
(d)
-dx.
²+1
r∞o 2² +1
24+1
c2π
dx.
(x2 + 2x + 2) (x²+4)
cos
2 + cos 0
(2-1)²(x+3)
1-sin(72/2)
-dx
do
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