Suppose that f and g are real valued functions defined on some interval (a,b) containing the point . Suppose also that and . Prove that if for all (for some ). Then . In this case is it always true that A<B.

For the first part my proof so far consists of a contradiction. I have assumed A>B and then proceded to write out the definitions of limit tending to with and so on. However I can't seem to find a contradiction and was wondering if someone could give me the first few lines I need.

I also have no idea for the second part. Thanks!