Thread: 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?

Originally Posted by Barthayn

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

Choose . If there exists such that if . But satisfies .

That is, (contradiction) .