Question
Find $\lim _{x \rightarrow 0} f(x)$, where $f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x \neq 0 \\ 0, & x=0\end{array}\right.$
Step 1
We know that $|x|$ is equal to $-x$ when $x<0$ and $x$ when $x>0$. So, we can rewrite $f(x)$ as follows: \[f(x)=\left\{\begin{array}{cc}-1, & x < 0 \\ 0, & x=0 \\ 1, & x > 0\end{array}\right.\] Show more…
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