Question

as x goes to infinite what is the limit of (e^x + x ) ^1/x

Answer 1

this is a tough one atleast for me

Answer 2

did you try this:
\[\text{ \let } y=(e^x+x)^\frac{1}{x}\]
\[\ln(y)=\frac{1}{x} \ln(e^x+x)\]
so \[y=e^{\ln(y)}=e^{\frac{1}{x}\ln(e^x+x)} \]
Then just
to find \[\lim_{x \rightarrow \infty }y=e^{\lim_{x \rightarrow \infty} \frac{\ln(e^x+x)}{x}}\]

Answer 3

then use l'hospital a couple of times