Math Help - Just read the "epsilon-delta proofs" topic

1. Just read the "epsilon-delta proofs" topic

Just read the "For those that never learnt well the epsilon-delta proofs" topic in this forum and through it I learned a lot of the proofs I never learned in class properly. However, I have a question. In the homework problem sets there are questions like prove the limit does not exist using the delta-epsilon definition. How does one do this?

For example, how would I show that the limit as x approaches 2 of 2x+1 is not 4?

2. Re: Just read the "epsilon-delta proofs" topic

Originally Posted by Barthayn
For example, how would I show that the limit as x approaches 2 of 2x+1 is not 4?
Choose $\epsilon=1$ . If $\lim_{x\to 2}(2x+1)=4$ there exists $\delta>0$ such that $|2x+1-4|=|2x-3|<1$ if $|x-2|<\delta$ . But $x=2+\delta/2$ satisfies $|x-2|<\delta$ .

That is, $|2x-3|=|4+\delta -3|=1+\delta<1$ (contradiction) .