Toronto Math Forum
MAT3342018F => MAT334Lectures & Home Assignments => Topic started by: Meerna Habeeb on November 12, 2018, 12:47:53 AM

I am not so sure about my work, can someone help and correct me if I am wrong, or add if I have something missing I should be adding it :) Thanks in advance

Here is my answer.
Hope it can help. :D

Post scans, not crappy snapshots

Hi, I got the similar results as yours. I think we are good.

Sin(z)=0
∴z=0 or z=kπ
When z=0,
Numerator: f(z)=z^2 ,f(0)=0
f'(z)=2z,f'(0)=0
f^'' (z)=2z ,f^'' (0)≠0
∴order=2
Denominator: g(z)=sinz ,g(0)=0
g^' (z)=cosz ,g^' (0)≠0
∴order=1
21=1
Order of zero=1
When z=kπ (k≠0)
Numerator: f(z)=z^2,f(kπ)=(kπ)^2≠0
∴order=0
Denominator: g(z)=sinz ,g(kπ)=0
g^' (z)=cosz ,g^' (kπ)≠0
∴order=1
10=1
It is simple pole.

the answer may like this