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Do someone know how could I calculate the following limit

$$\lim_{x\to0} \frac{e-(1+x)^{1/x}}{x}$$ when x goes to zero. e is Napier.

Lutz Lehmann
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maryam
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    cf : http://math.stackexchange.com/questions/879085/another-method-for-limit-of-e-1x1-x-x-as-x-approaches-zero – mathlove Oct 19 '15 at 18:28

1 Answers1

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You can compute this as

  • the limit of a difference quotient for $f(x)=(1+x)^{1/x}$ or

  • via the power series of logarithm and exponential.

Lutz Lehmann
  • 126,666