How to solve this?

[plain nova]

I tried l'hopital's rule but i still dont know have any idea how to evaluate this limit. The calculator says e and idk why

[carmine geyser]

this can be restated at the limit from X to +infinity of (1+1/x)^x

which is one of the definitions for e

because the individual limits for x going to zero of x and x going to infinity of 1/x are both 0, and the limits of x going to infinity of X and x going to +0 of 1/x are both infinity

@plain nova

[hollow marsh]

It actually doesn't even need to be 0+. The limit as x approaches 0 from either side is e.

[celest grove]

let $n = 1/x$ \
then the limit becomes $\lim_{n \to \infty} (1+1/n)^n = e$