Answer
-5
Work Step by Step
Have your book open on pp.716-717, so you have
"Some Determinate and lndeterminate Forms" and "Strategy for Evaluating Limits Algebraically" available.
steps from the "Strategy":
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 x, we evaluate: $f(-1)=\displaystyle \frac{4(-1)^{2}+1}{-1}=\frac{5}{-1}=-5$
and, we're done.
$\displaystyle \lim_{x\rightarrow-1}f(x) =-5$
