Practicing Success
Practicing Success
CUET Preparation Today
| Define a function $f:\mathbb{R}\rightarrow \mathbb{R}$ as $f(x)=\begin{cases}\frac{x}{|x|}& \text{if}\hspace{.2cm} x \neq 0\\ 0,& \text{otherwise} \end{cases}$. Then $f$ is |
Continuous at 0 Discontinuous at 0 Differentiable at 0 None of the above |
| Discontinuous at 0 |
| $f$ is discontinuous at 0 because $\lim_{x \to 0+}f(x)=1$ ,$\lim_{x \to 0-}f(x)=-1$ and $f(0)=0$. |
