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## #1 Help Me ! » Discontinuous Function » 2014-11-03 15:18:42

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!

## #2 Re: Help Me ! » Sequence Limit Proof » 2014-10-08 02:25:16

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

## #3 Re: Help Me ! » Sequence Limit Proof » 2014-10-07 15:33:30

Is there some way to define N as the minimum of two values (one being the value I already found), that would make this possible? I am completely stuck on this one. I can't figure out where to go with it

## #4 Help Me ! » Sequence Limit Proof » 2014-10-06 18:23:43

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.

## #23 Re: Puzzles and Games » Add 99 more and post it forever. » 2014-07-11 13:31:20

144540 - 1 = 144539 is prime
144540 + 1 = 144541 is prime