Answer
$\displaystyle \lim_{\mathrm{x}\rightarrow 1}f(x)=0$
Work Step by Step
Follow the steps in "Evaluating Limits Graphically"
(steps 3-5: one-sided limits, limit at x=a)
x=1
As we trace the graph on either side of x=$1$
(approaching x=1, but not $1$ itself),
the points on the graph approach the point $(1,0),$
f(x) approaches $0$ (from either side), so
both one-sided limits exist and equal $0$,
the limit $\displaystyle \lim_{\mathrm{x}\rightarrow 1}f(x)$ exists, and
$\displaystyle \lim_{\mathrm{x}\rightarrow 1}f(x)=0$
