Consider
\[f(x)=\frac{(x \log x+x)^{5}(1+2 / x)^{x}}{(x+1 / x)^{5}(\log x+1 / \log x)^{6}}\]
What can we say about $\lim _{x \rightarrow \infty} f(x)$ ?
- The function $f(x)$ does not have a limit as $x \rightarrow \infty$
- $\lim _{x \rightarrow \infty} f(x)=e^{2}$
- $\lim _{x \rightarrow \infty} f(x)=e^{1 / 2}$
- $\lim _{x \rightarrow \infty} f(x)=0$
- $\lim _{x \rightarrow \infty} f(x)=\infty$