let-f-z-cos-3z-z-2-calculate-Res-f-0-

Question Number 63084 by mathmax by abdo last updated on 28/Jun/19

l e t f (z) = \frac{c o s (3 z)}{z^{2}}

c a l c u l a t e R e s (f, 0) .

Commented by mathmax by abdo last updated on 01/Jul/19

0 i s p o l e o f f w i t h o r d r 2 \Rightarrow R e s (f, 0) = {l i m}_{z \to 0} \frac{1}{(2 - 1)!} {z^{2} f (z)}^{(1)}

= {l i m}_{z \to 0} {c o s (3 z)}^{(1)} = {l i m}_{z \to 0} {- 3 s i n (3 z)} = 0 .