![enter image description here](https://i.stack.imgur.com/NhEHr.jpg)

<http://s23.postimg.org/xedyol4kr/limit.jpg>

I got stuck on Q2 , could someone shed light on how to do it? The proof bit. Finding limits in terms of α and β is easy.

As for Q3, I know it is probably not the way I was supposed to do but is the following method not correct?
Lim (A+B)= lim(a)+lim(b) and we are given that lim(a)=∞ and lim(b) is bounded below hence it is converging to some numerical value L. So lim(a)+lim(b)= ∞+L=∞ ? 
Many thanks