Question

\[\lim_{x \to\infty}xe^{\frac{ 1 }{ x }}-x\]

Answer 1

or more to the point, why is it 1?

Answer 2

holy cow! wut is this math

Answer 3

or more more to the point, why is it 1 without using power series?

Answer 4

Hum did you try finding the first derivative?

Answer 5

\[\Large \lim_{x\to \infty}(xe^{1/x} - x)\]
\[\Large \lim_{x\to \infty}(x(e^{1/x} - 1))\]
\[\Large \lim_{x\to \infty}\left(\frac{e^{1/x} - 1}{1/x}\right)\]
then use L'Hospitals rule

Answer 6

oh wow thanks !

Answer 7

no problem

Answer 8

old trick i forgot to use here
the form was messing me up

Answer 9

yeah I had to look it up myself a while back. It has to be in the form f/g

Answer 10

thanks guys