Question

If $f\left(x\right)=\{\begin{array}{cc}1& x<0\\ x^2& x\ge 0\end{array}$ then at $x=0$

• A. $f$ is not differentiable
• B. $f$ is continuous
• C. $f$ is differentiable
• D. $f$ is not continuous

Answer 1

Answer: (D)

$f$ is not continuous

$f\left(x\right)=\{\begin{array}{c}1,x<0\\ x^2,x\ge 0\end{array}$

$\underset{x\to 0^{+}}{lim}f\left(x\right)=\underset{x\to 0}{lim}{x}^2=0$

$\underset{x\to 0^{-}}{lim}f\left(x\right)=\underset{x\to 0}{lim}1=1$

$SinceR.H.L\ne L.H.latx=0$

So $f\left(x\right)$ is not Continuous at $x=0$