Limits involving $e$

Question

I am looking to solve the following limits.

$\displaystyle\lim_{x\to-\infty}5e^{-x}$

and

$\displaystyle\lim_{x\to2}\frac{1}{2e-ex}$

Any help would be appreciated.

Answer 1

The first limit diverges to $\infty$. You can see this by looking at the graph.

Also, for the second limit, when $x \to 2^+$, it diverges to $-\infty$, when $x \to 2^-$, it diverges to $\infty$.

The left and right limits are not the same, so the second limit does not exist.