I am having trouble starting a problem on the continuity of a function. The problem is:
I think that the intermediate value theorem would be useful in the proof, but I can't figure out how to apply it. Does anybody have an idea for something that could be useful for this problem? Thanks for any help!
Hello. I am trying to prove the limit of a sequence using the definition of a sequence limit. The definition is:
I am trying to prove that
This is what I have done so far:
The issue I am having is that by the definition, epsilon can be any positive number. But by the value I have given N through manipulating these equations, epsilon cannot be equal to 2. Is this allowed? If not, is there some other method of finding such an N?
I appreciate any input! Thanks.