Singularities and integrating

Hi, I have some past papers with no answers and not much idea on how to find them, any help appreciated!!

For part a) is it something about lies on the circle with radius and so its minimal distance to -sqrt(2)a i ?

part b) use the M-L lemma to show int(f) / which tends to zero as tends to infinity?

c) singularities would be though not sure what these are . Think I may have to brake down into composite parts e.g.

part d) I have no idea!

http://www.eussc.com/images/q6.jpg