Advanced Calculus question.

[xThai]

For #1, I have no idea how to approach this... I've literally looked at it for an hour without any idea how to do it.

For #2, I just proved this by using the squeeze theorem proof, using epsilon and delta. I'm hoping it's correct, but I'm supposed that the limit of g(x) as x -> a exists. (p.s. the last part is a typo and it's supposed to say g(x)). So I don't think the way I did it is correct.

Any help?

[windsurfer-sp]

Problem 2. If f<g<h, and if f=h then f=g. Have fun solving with delta and epsilon.

[dore]

The second one is asking you to prove the squeeze theorem, so no you couldn't just use the squeeze theorem . But for that one you basically just have to use the definition of limits (using your greek letters ofc) on f and h and then use the fact that if g(a) > f(a) and g(a) < h(a) and f(a) = h(a) then g(a) = f(a) = h(a). It's a self-writing proof if you just write out your definitions of your givens and work them toward the destination which conclude in having the greek letter definition of limits existing for g.