Question

What is the limit as x approaches infinity of x^1/x

Answer 1

start with
\[x^{\frac{1}{x}}=e^{\frac{1}{x}\ln(x)}\] so your job is to find
\[\lim_{x\to \infty}\frac{\ln(x)}{x}\] then raise \(e\) to that number

Answer 2

if you plug that equation into a graphing calculator you can then see the end behavior and then write the limit i hope this helps. :)

Answer 3

\[\lim_{x\to \infty}\frac{\ln(x)}{x}=0\] pretty much from your eyeyballs
then you get \(e^0=1\)