Answer
See the proof below.
Work Step by Step
Since $f(x)\leq|f(x)|$ and $f(x)\geq-|f(x)|$, then we get
$-|f(x)|\leq f(x)\leq |f(x)|$
We have
$\lim\limits_{x \to c}|f(x)|=\lim\limits_{x \to c}-|f(x)|=0$
Then by the Squeeze Theorem, we get
$\lim\limits_{x \to c} f(x)=0$
Therefore
if $\lim\limits_{x \to c}|f(x)|=0$, then $\lim\limits_{x \to c} f(x)=0$.
