Evaluating the limit $\lim_{n \rightarrow +\infty} \frac{e^n+e^{-n}}{e^{n+1}+e^{-n-1}}$ How would you solve the following limit? It's $\frac \infty \infty$ and L'Hospital doesn't seem to help:
$$\lim_{n \rightarrow +\infty} \frac{e^n+e^{-n}}{e^{n+1}+e^{-n-1}}$$

Intuition: As $n$ gets very large, $e^{-n}$ and $e^{-n-1}$ both get very, very small, so what you're left with should be 
$$\lim_{n\to\infty} \frac{e^n}{e^{n+1}}.$$
