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Derivative using l'hopital's rule

  1. Apr 29, 2010 #1
    let f(x)

    exp(-1/x) for x>0, 0 for x<=0

    i want to get f'(x) by using l'hopital's rule, but somehow

    i'm applying l'hopital's rule again and again and no clear value is coming out.

    i know f'(0) is 0, but i cannot prove it
  2. jcsd
  3. Apr 29, 2010 #2
    So, using the definition of the derivative, you're looking for the limit as x-->0 of exp(-1/x)/x.

    If you use L'Hopital on this, you get that it is equal to the limit as x-->0 of -exp(-1/x)/x.

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