## DLS Group Title Limits question [Challenge] one year ago one year ago

1. DLS Group Title

$\LARGE \lim_{x \rightarrow 0} \frac{(1+x)^\frac{1}{x} -e}{x}$

2. DLS Group Title

@yrelhan4 @shubhamsrg

3. shubhamsrg Group Title

* :)

4. DLS Group Title

first time in life :O

5. ParthKohli Group Title

Taylor Series expansion?

6. DLS Group Title

Use whatever you want.

7. ParthKohli Group Title

Ans 0?

8. DLS Group Title

Nope

9. experimentX Group Title

Taylor series works

10. ParthKohli Group Title

Weird. The Taylor Series expansion is in the terms of $$e$$ and $$x$$. The first term is $$e$$

11. DLS Group Title

Taylor series gives 0?

12. experimentX Group Title

gives -e/2 if you calculate correctly

13. ParthKohli Group Title

Oh wait! lol, yeah. I forgot to consider that -e/2 which had no $$x$$

14. DLS Group Title

How about a different way rather than taylor series?

15. ParthKohli Group Title

Definition of derivative? :-|

16. DLS Group Title

o.O

17. ParthKohli Group Title

I was just thinking how this might be the definition of a derivative in disguise.

18. experimentX Group Title

Binomial expansion might work ... but that's too long

19. ParthKohli Group Title

DLS Use whatever you want. 15 minutes ago DLS How about a different way rather than taylor series? 9 minutes ago

20. DLS Group Title

You are right,still investigating for more methods,I wrote so to specify that you are not bound to any particular method,just asking if you know anything alternate :)

21. experimentX Group Title

L'hopital works

22. experimentX Group Title

http://www.wolframalpha.com/input/?i=Limit%5B%281+%2B+x%29%5E%281%2Fx%29+%281%2F%28x+%281+%2B+x%29%29+-+Log%5B1+%2B+x%5D%2Fx%5E2%29%2C+x+-%3E+0%5D after using L'hopital you get this expression. The first term tends to e .. if you again apply L'hopital on the second term, you will get -1/2