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Limit of e^(1/x) as x->0

  1. Jan 9, 2017 #1
    1cbf4ac287084491ad5b7ed95f9ed522.jpg
    In this solution, in the last 3rd line, I get the first part (-e^-1 - e^-1), however, after the '-' symbol, the person writes (1/b * e^1/b - e^1/b) and takes the limit as b->0. However, shouldn't this give him (inf. * e^inf - e^inf)?

    Thanks
    (His answer is correct, by the way)
     
  2. jcsd
  3. Jan 9, 2017 #2

    haruspex

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    b approaches 0 from below, so 1/b tends to minus infinity. There is a small mistake: the 1 in the (1 . 0 - 0) term. Need to use the fact that x e-x tends to 0 as x tends to +infinity.
     
  4. Jan 9, 2017 #3
    Ohk! I didn't notice the fact that we were approaching 0 from the left hand side. Thanks! :)
     
  5. Jan 9, 2017 #4

    Ray Vickson

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    Right: if you approach 0 from the right the function blows up: ##\lim_{x \to 0+} e^{1/x} = +\infty##.
     
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