Question

question on limits!

Answer 1

\[\lim_{x \rightarrow \infty} (1+\frac{ 1 }{ x })^{\ln x}\]

Answer 2

rewrite as
\[\large e^{\ln(x)\ln(1+\frac{1}{x})}\] and then use l'hopital to compute the limit of
\[\lim_{x\to \infty}\ln(x)\ln(1+\frac{1}{x})\]

Answer 3

now it is in the form \(\infty\times 0\)
usual gimmick is a trick of algebra to rewrite it as
\[\frac{\ln(1+\frac{1}{x})}{\frac{1}{\ln(x)}}\]

Answer 4

you good from there?

Answer 5

yah i think i got it from there thanks