Answer
please see step-by-step
Work Step by Step
We solve this applying the Squeeze Theorem,
If $f(x) \leq g(x) \leq h(x)$ when $x$ is near $a$ (except possibly at a)
and $\displaystyle \lim_{x\rightarrow a}f(x)=\lim_{x\rightarrow a}h(x)=L$
then $\displaystyle \lim_{x\rightarrow a}g(x)=L$
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Let $u(x)=0,\qquad v(x)=x^{2}$ for all x.
Then,
$u(x) \leq f(x) \leq v(x)$ for all $x$.
Also,
$\displaystyle \lim_{x\rightarrow 0}u(x)= \displaystyle \lim_{x\rightarrow 0}0=0$
$\displaystyle \lim_{x\rightarrow 0}v(x)=\lim_{x\rightarrow 0}x^{2}=0,$
So, by the Squeeze Theorem, $\displaystyle \lim_{x\rightarrow 0}f(x)=0$.
