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

  1. #1
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    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?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Just read the "epsilon-delta proofs" topic

    Quote Originally Posted by Barthayn View Post
    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) .
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