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No limit

  1. Oct 2, 2007 #1
    f(x)=1,xeQ
    f(x)=0,x in not eQ

    It's easy to understand that this function has no limit as x tends to 0,but how we can prove it with mathematical formulas.

    And what's the lim[e^n-(1+1/n)^n^2]
     
    Last edited: Oct 2, 2007
  2. jcsd
  3. Oct 2, 2007 #2

    quasar987

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    Prove it with the definition of limit.

    Can you find an epsilon such that no delta-nbhd of 0 is mapped entirely in an epsilon-nbhd of f(0)=1?

    Or use the characterisation in terms of sequences. The limit is f(0) iff for every sequence converginf to 0, the image sequence converges to f(0). Can you find a sequence such that the image sequence does not converge to f(0)?
     
    Last edited: Oct 2, 2007
  4. Oct 3, 2007 #3
    quasar987,
    I could not solve with sequences.Can u plz post the solution.
     
  5. Oct 3, 2007 #4

    HallsofIvy

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    So far you haven't shown that you have tried anything at all! What have you tried?

    Have you thought about what f(x) is if x is close to 0 and rational?
    What f(x) is if x is close to 0 and irrational?
    COULD f(x) be "close" to some limit if x is any number close to 0?
     
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