Answer
4
Work Step by Step
1. f is a closed function (we know by Th.10.1 that it is continuous), that is, L= $\displaystyle \lim_{x\rightarrow a}f(x)$ = $f(a)$,
for all a from the domain of f.
2. substituting $1$ for $h$, we evaluate: $f(1)=(1^{2}+2(1)+1)=4$
and, we're done.
$\displaystyle \lim_{h\rightarrow 1}f(h) =4$
