Question

Solve the exponential limit
http://i.imgur.com/RHzNK7L.png

Answer 1

Please apply l'Hopital's Rule here. If you have problems with that, please ask questions.

Answer 2

I'm not supposed to use l'hopital's rule. I'm supposed to use substitution

Answer 3

I assume you know
\[ \lim_{x\rightarrow \infty} \left( 1+\frac{1}{x}\right)^x \]

let u =2x in your problem
and put your expression in terms of u
what do you get ?

Answer 4

Supposing we set u=2x as phi has suggested.
Solve for x. x = ??

In:
\[\lim_{x\rightarrow \infty} \left( 1+\frac{1}{x}\right)^x\]

Answer 5

that \[\lim_{x\rightarrow \infty}\]

Answer 6

now becomes \[\lim_{u\rightarrow \infty}\]

Answer 7

Can you now finish re-writing phi's \[\lim_{x\rightarrow \infty} \left( 1+\frac{1}{x}\right)^x\] ... in terms of u?

Answer 8

none of this was helpful at all

Answer 9

The first step is

let u =2x in your problem
and put your expression in terms of u
what do you get ?