Question

Limits question [Challenge]

Answer 1

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

Answer 2

@yrelhan4 @shubhamsrg

Answer 3

*

:)

Answer 4

first time in life :O

Answer 5

Taylor Series expansion?

Answer 6

Use whatever you want.

Answer 7

Ans 0?

Answer 8

Nope

Answer 9

Taylor series works

Answer 10

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

Answer 11

Taylor series gives 0?

Answer 12

gives -e/2 if you calculate correctly

Answer 13

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

Answer 14

How about a different way rather than taylor series?

Answer 15

Definition of derivative? :-|

Answer 16

o.O

Answer 17

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

Answer 18

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

Answer 19

DLS
Use whatever you want.
15 minutes ago


DLS
How about a different way rather than taylor series?
9 minutes ago

Answer 20

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 :)

Answer 21

L'hopital works

Answer 22

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