Hello everyone this was a problem on one of the exams from last year and I'm having trouble with the last point ##3##
my solution for ##1##
$$\frac{1}{2\pi i}\int_{|z|=r}\frac{f(z)}{z}(1+\frac{z}{2re^{i\theta}}+\frac{re^{i\theta}}{2z})dz =$$
I divided this integral into 3 different ones and...