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**Maburo**- Replies: 0

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!

Very clever! That was awesome. Now I suppose I should practice coming up with such things on spot.

Thanks for your help!

**Maburo**- Replies: 5

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.

144540 - 1 = 144539 is prime

144540 + 1 = 144541 is prime