5.19. In this problem f(z) = P and R > 1. Modify our computations in Example 5.14 as follows. exp(iz) z²+1 YR (b) Show that |exp(iz)| < 1 for z in the upper half plane, and conclude that |f (z)| < for sufficiently large |z|. -R R (c) Show that limr→∞ = 0 and hence limr-00 Si f = %. -R,R] (d) Conclude, by just considering the real part, that cos(x) dx = e -00
5.19. In this problem f(z) = P and R > 1. Modify our computations in Example 5.14 as follows. exp(iz) z²+1 YR (b) Show that |exp(iz)| < 1 for z in the upper half plane, and conclude that |f (z)| < for sufficiently large |z|. -R R (c) Show that limr→∞ = 0 and hence limr-00 Si f = %. -R,R] (d) Conclude, by just considering the real part, that cos(x) dx = e -00
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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Complex Variables - Only need B, C, and D, thank you.

Transcribed Image Text:5.19. In this problem f(z)
exp(iz)
p and R > 1. Modify our computations in Example 5.14 as
z2+1
follows.
YR
(b) Show that |exp(iz)| < 1 for z in the upper half plane, and conclude that |f(z)| <
for
sufficiently large |z|.
-R
R
(c) Show that limr-0 Soa f = 0 and hence limr→00
Si-R,R} ƒ = =.
(d) Conclude, by just considering the real part, that
cos(x)
dx =
x² + 1
e
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