Answered: [1 + (- P] f S + (−1)²] XP 1+x² XP 1+x²…

[1 + (- P] f S + (−1)²] XP 1+x² XP 1+x² dx = implifying and using the given formula for the pth root, we obtain ( TU dx COS = лр 2 2ni Res(f; i) = ni². -1 " -1 < p < 1.

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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Question

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I was able to get the first result in the sentence that starts "The conclusion is that....", but I do not understand how the simplification was done after that. How did they get the part that starts with "Simplifying and using the given formula..." Is there an identity for [1+(-1)^p] that I need to use?

which goes to zero as & →0. We apply the Residue Theorem and then let & →
R→ ∞o. The conclusion is that
> 0 and
[1 + (−1)²]
ܐܬ݂ܳ1]
XP
+x²
XP
dx
1 + x²
dx =
Simplifying and using the given formula for the pth root, we obtain
-1
So
<= 171 (COSTP) ²¹.
2лi Res(f; i) = niº.
-1 < p < 1.
0

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