Find the limit as x --> +inf

This limit is of the form $1^{\infty}$
The limits of the same form generalised as shown
$$\lim_{x\to\infty}(1+f(x))^{g(x)}$$ can be solved using the formula
$$\lim_{x\to\infty}(1+f(x))^{g(x)}=e^{\lim_{x\to\infty}f(x)g(x)}$$
Thus we get
$$\lim_{x\to\infty}(1+\frac1x)^{x}=e^{\lim_{x\to\infty}\frac1x \cdot x}=e^1=\boxed e$$