## anonymous 5 years ago lim (1 - 1/x)^(-x) as x->+infinty

1. anonymous

= 0

2. anonymous

can you please explain to me how you got that

3. anonymous

I can.

4. anonymous

if you let x = infinity. Then what is 1/x really equal to?

5. anonymous

It's wrong though.

6. anonymous

My solution? Please correct me then sir.

7. anonymous

I think this is a special identity representing e, but let me check.

8. anonymous

If my Cal I recall is correct, if the exponent was positive, it is the well-recognized lim that goes to e. The fact that exponent is is negative, I am leaning to agree with you it goes to 0. How did you reach your conclusion.

9. anonymous

Well, You have something that is always smaller than one being raised to big negative numbers. It will certainly not tend toward 0 because the exponentiation will grow faster than the -1/x will shrink. However I think it does converge on e rather than go on to infinity.

10. anonymous

It's 1-1, how do you get -1? And it's to the -x, meaning the equation is actually 1/(1-1/x) which is certainly zero.

11. anonymous

No. It is $(1-\frac{1}{x})^{-x}$ I agree that the fraction will tend toward 0, but the whole expression tends toward $$1^\infty$$

12. anonymous

Actually I contend that inside the bracket goes to 1 because $(1 \div \infty)$ tends to zero.

13. anonymous

Oh my bad didn't see 1-1/x, even then the resultant inside is still zero. 0^infinity = 0.

14. anonymous

it's not $$1-\infty$$ it is 1- 0

15. anonymous

God I need to stop failing and go to bed lol. I'm sorry polpak you're right.

16. anonymous

But that is leaves us with $$\frac{1}{1^\infty}$$ which is undetermined form and needs special handling with l'hopital.

17. anonymous

Have to take the log to bring down the x out of the exponent, then take the derivative, etc. It's kind of a bear. It looks like it might be e though.

18. anonymous

We need Lokisan for this one. We need someone who has read everything concerning the number or the limit e.

19. anonymous

Heh. Well I checked with Alpha, and it's definitely e. Glad I don't have to do this for my homework though.

20. anonymous
21. anonymous

Good job.