Mathematical Analysis - Continuity

[rollsroy]

Homework Statement

Homework Equations

The Attempt at a Solution

Basically the first part of the question asks to prove the binomial theorem through induction which I've done.

I'm basically lost as to how to even attempt these questions, I'm not asking for answers as I need to know this stuff for exams and other courses.

Can anyone point me to a place where I can find similar style of questions with an explanation on the theory on how to do them?

We've only been shown in lectures on how to show continuity through epsilon-delta arguments?

 

[rollsroy]

anyone?