Complex Integral Residue Theorem

[Tangent87]

I have attached a pdf of my problem and attempted solution. I seem to be a factor of f'(z) out from the required solution, can anyone see where I've gone wrong?

 

[Dick]

Yes, shouldn't the expression you are taking the limit of to get the residue be (t-z)*t*f'(t)/(f(t)-w)?

 

[Tangent87]

Ahh yeah crap, I was thinking f(t)-w would cancel as usual when taking a residue of a simple pole but it's f(t) not t. Cheers.