the limits if it exists, if it does not explain why. (1) lim ()" (ii) lim

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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4. (a) Find the limits if it exists, if it does not explain why.
(1) lim ("
(ii) lim
n 00
(b) (i) Let R be the radius of convergence of the power series an(z – z.)" and suppose that
n=0
ant1
lim
n 00
L exists, for some real number L, show that R = }.
%3D
an
(ii) Find the radius of convergence of the series
E(z - ni)", hence, find the region about
z = ni where the series converges.
(c) Let z and w be none zero complex numbers. Prove that | z+ w - | z – w = 4Re(zw).
Transcribed Image Text:4. (a) Find the limits if it exists, if it does not explain why. (1) lim (" (ii) lim n 00 (b) (i) Let R be the radius of convergence of the power series an(z – z.)" and suppose that n=0 ant1 lim n 00 L exists, for some real number L, show that R = }. %3D an (ii) Find the radius of convergence of the series E(z - ni)", hence, find the region about z = ni where the series converges. (c) Let z and w be none zero complex numbers. Prove that | z+ w - | z – w = 4Re(zw).
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