Answer
The limit does not exist.
Work Step by Step
Please see image attached
for the values that need to be entered into the table.
Reading the table,
as $x$ approaches $1$ from the left,
$h(x)$ seems to rise without bound, $\displaystyle \lim_{x\rightarrow 1^{-}}h(x)=+\infty$
as $x$ approaches $1$ from the right,
$h(x)$seems to descend without bound, $\displaystyle \lim_{x\rightarrow 1^{+}}h(x)=-\infty$
so we estimate that
$\displaystyle \lim_{x\rightarrow 1}h(x)$ does not exist.
