Why is L'Hôpital's rule giving the wrong answer? Given the following limit:
$$
 \lim_{x \rightarrow -1}  \frac{x^5+1}{x+1} 
$$
The solution using L'Hôpital's rule:
$$
 \lim_{x \rightarrow -1}  \frac{x^5+1}{x+1} = \begin{pmatrix} \frac{0}{0} \end{pmatrix} \rightarrow \lim_{x \rightarrow -1}  \frac{5x^4}{1} = 5 \cdot (-1)^4 = -5  
$$
This is wrong. How come?
EDIT: Well, a perfect example of a huge blunder.

It's because $$(-1)^4=1.$$ ${}$
