anonymous 5 years ago find limx^(1/(1-e^-x) when x --> 0

1. anonymous

$\lim_{x \rightarrow 0}x ^{1/(1-e ^{-x})}$

2. anonymous

$\lim_{x \rightarrow 0}x ^{1/\ln (1-e ^{-x})}$

3. anonymous

the last one is correct

4. anonymous

Take it piece by piece$e ^{0}$is what?

5. anonymous

it's 1

6. anonymous

$\ln (1-1)$=What is $\ln 0$It is a trick question.

7. anonymous

$-\infty$

8. anonymous

?

9. 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?

10. anonymous

I got x^0, but x goes to 0, so I got 0^0

11. 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?

12. anonymous

I don't understand what do you want to say, I am not so good with English. Can you just write solution?

13. anonymous

$\ln y =\ln x ^{1/\ln(1-e ^{-x)}}$

14. anonymous

and now I have to find limes of this? That's all? :)

15. anonymous

Take lim of each side

16. anonymous

ok :) thank you very much :)

17. anonymous

I forgot: L'hopital

18. anonymous

what L'hopital ? :)

19. anonymous

L'hopital = 1) derivative, 2) limit. Does not work here.