Complex analysis: Residue Theorem, ML Lemma, and Limit

Please help me with the following problems:

(My TA says ML lemma is helpful for problem 3&4)

So we have four parts: a. large circle of radius R, a small circle of radius r, and the line segment from R to r, and the line segment from 1' to R (which occupies the same location in the complex plane as the other line segment, which is why there are two arrows drawn there on the diagram). The function we are going to integrate is 28-1 e(s-1) log(=) f ( 2 ) = 1+2 1+2 Here we are going to use a different convention for log(2) to the principal logarithm: we are going to take 0 0 and R - co. Let s = a + ib. 3. Show that f(z)dz