MCQ_SINGLE

The function f defined by \(f(x)=\begin{cases}x,&if~x\le1\\ 5,&if~x>1\end{cases}\) is not continuous at:

SA

Find the value of a and b so that function f defined as : $$ f(x) = \begin{cases} \frac{x-2}{|x-2|} + a, & \text{if } x < 2 \\ a+b, & \text{if } x = 2 \\ \frac{x-2}{|x-2|} + b, & \text{if } x > 2 \end{cases} $$ is a continuous function.

VSA

Check whether the function $f(x)=x^{2}|x|$ is differentiable at $x=0$ or not.

MCQ_SINGLE

A function \(f(x)=|1-x+|x||\) is:

VSA

Verify whether the function f defined by $f(x)=\begin{cases}x~sin(\frac{1}{x}),x\ne0\\ 0&,x=0\end{cases}$ is continuous at $x=0$ or not.

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