Gg
  • Gg
find limx^(1/(1-e^-x) when x --> 0
Mathematics
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Gg
  • Gg
find limx^(1/(1-e^-x) when x --> 0
Mathematics
schrodinger
  • schrodinger
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Gg
  • Gg
\[\lim_{x \rightarrow 0}x ^{1/(1-e ^{-x})}\]
Gg
  • Gg
\[\lim_{x \rightarrow 0}x ^{1/\ln (1-e ^{-x})}\]
Gg
  • Gg
the last one is correct

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anonymous
  • anonymous
Take it piece by piece\[e ^{0}\]is what?
Gg
  • Gg
it's 1
anonymous
  • anonymous
\[\ln (1-1)\]=What is \[\ln 0\]It is a trick question.
Gg
  • Gg
\[-\infty\]
Gg
  • Gg
?
anonymous
  • anonymous
Great. I never got that right each time my teacher asked. You are ahead of the game. So put it together, what is the answer?
Gg
  • Gg
I got x^0, but x goes to 0, so I got 0^0
anonymous
  • anonymous
Actually 1 over 0 to the power of infinity, I think. Either way our little game ended in a indeterminate form. This is one where you set y equal to your original thingy. Take ln y and take ln of your thingy. You ever did any of those?
Gg
  • Gg
I don't understand what do you want to say, I am not so good with English. Can you just write solution?
anonymous
  • anonymous
\[\ln y =\ln x ^{1/\ln(1-e ^{-x)}}\]
Gg
  • Gg
and now I have to find limes of this? That's all? :)
anonymous
  • anonymous
Take lim of each side
Gg
  • Gg
ok :) thank you very much :)
anonymous
  • anonymous
I forgot: L'hopital
Gg
  • Gg
what L'hopital ? :)
anonymous
  • anonymous
L'hopital = 1) derivative, 2) limit. Does not work here.

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