(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This was an exam question I had today:

Give the location and order of each pole of

f(z)=e^z/[(z-1)^2(z+2)]

and evaluate the reside at these points

2. Relevant equations

Res(f(z)) = g(p-1)(a) / (p-1)!

3. The attempt at a solution

g(z) = e^z/(z+2)

g'(z) = -e^z/(z+2)^2

let a=1

g'(1) = -e^1/9

So res(f,1) = -e/9

Then I did

g(z) = e^z/(z-1)^2

(this is the part I think I might have stuffed up, because I did use the formula above but I had m=1 for f(z) which was 1/(z+2) so I thought it was right??? anyways I got

g(-2) = e^(-2) / (-3)^2 = res(f,-2)=1/(9e^2)

It would mean a lot to me if someone could let me know because I am trying to work out if I should be depressed because I failed or if I can be happy because I passed :)

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# Homework Help: Is this the answer for what is the residue of f(z)=e^z/[(z-1)^2(z+2)]

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