Question: Evaluate $\lim\_{x\to \infty}(1+\frac{1}{\sqrt{x}})^x$

This is an exercise in my analysis book and I'm having trouble solving it. It's clearly related to the limit of $e$. I've tried rewriting:

Evaluate $\lim\_{x\to \infty}((1+\frac{1}{\sqrt{x}})^\sqrt{x})^\sqrt{x}$.

Now I sadly cannot rewrite this as $\lim\_{x\to \infty}(e)^x$ or anything similar. Thoughts?

Answer: 
Hint. Note that as $x\to +\infty$,
$$\left(1+\frac{1}{\sqrt{x}}\right)^x=\exp\left(x\ln\left(1+\frac{1}{\sqrt{x}}\right)\right)\sim \exp\left(\frac{x}{\sqrt{x}}\right)=\exp\left(\sqrt{x}\right)$$
wher we use the fact that $\ln(1+t)\sim t$ as $t\to 0$.
It is not hard to show that for $x>1$, $$\left(1+\frac1{\sqrt x}\right)^{\sqrt x}>2$$ and your limit is $\infty$.