Here is the problem:
how would i prove this? I am very lost in this course
As lost as you can be, I bet you're not as lost as to be unable to check one of the 834572034584834 books of calculus there are: this one is a very simple and standard theorem, also called the sandwich theorem, and any decent basic calculus book must include it. Now do a search in your library and/or in google!
Tonio