Answer
0
Work Step by Step
$ f(-1)=\frac{(-1)^{2}+2(-1)+1}{-1+1}=\frac{0}{0}$
The function has the indeterminate form $\frac{0}{0}$ at x=-1.
Transforming algebraically and canceling, we have
$\frac{x^{2}+2x+1}{x+1}=\frac{(x+1)(x+1)}{x+1}=x+1$
Evaluating using continuity, we get
$\lim\limits_{x \to -1}\frac{x^{2}+2x+1}{x+1}=\lim\limits_{x \to -1}(x+1)=-1+1=0$
