Toronto Math Forum

MAT334-2018F => MAT334--Lectures & Home Assignments => Topic started by: Meerna Habeeb on November 12, 2018, 12:47:53 AM

Title: Question 2 from 2.5
Post 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
Title: Re: Question 2 from 2.5
Post by: Yexuan Zhang on November 12, 2018, 01:57:47 AM
Here is my answer.
Hope it can help. :D
Title: Re: Question 2 from 2.5
Post by: Victor Ivrii on November 12, 2018, 03:15:47 AM
Post scans, not crappy snapshots
Title: Re: Question 2 from 2.5
Post by: Zhijian Zhu on November 12, 2018, 10:37:05 AM
Hi, I got the similar results as yours. I think we are good.
Title: Re: Question 2 from 2.5
Post by: Huanglei Ln on November 14, 2018, 03:12:53 PM
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
2-1=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
1-0=1
It is simple pole.
Title: Re: Question 2 from 2.5
Post by: Huanglei Ln on November 14, 2018, 03:18:38 PM
the answer may like this