I have a couple of problems due soon that I need help comprehending.

Firstly, I need to prove the Squeeze Theorem using the formal (Epsilon-Delta) definition of limits. I've read the actual proof from Wikipedia, but I just can't wrap my head around it, it feels like they're skipping some sort've explination in certain parts.

For example, on the Wiki page (Squeeze theorem - Wikipedia, the free encyclopedia) it gets to a point where they give , then jump down and say that this proves , but I don't see how they got from one step to the other.

Then, while they prove the general case, they have and end up with . I understand the two steps they show in between, but I don't see how using those two steps results in the latter equation.

Secondly, I need to prove that: lim x->infinity f(x) is equal to lim x->0+ f(1/x), not intuitively, but using:

The definition of lim x-> infinity f(x) = L is: for all epsilon > 0 there exists an N > 0 such that x > N -> |f(x)-L| < epsilon.

Preemptive thanks for the help!