VSA

Show that the function $f(x)=\begin{cases}\frac{\cos x}{-x+\frac{\pi}{2}}, & x\ne\frac{\pi}{2} \\ 1, & x=\frac{\pi}{2}\end{cases}$ is continuous at $x=\frac{\pi}{2}$.

MCQ_SINGLE

The value of k for which function $f(x)=\begin{cases}x^{2},&x\ge0\\ kx,&x

VSA

If $y=(x+\sqrt{x^{2}-1})^{2}$;, then show that $(x^{2}-1)(\frac{dy}{dx})^{2}=4y^{2}.$

MCQ_SINGLE

If A denotes the set of continuous functions and B denotes set of differentiable functions, then which of the following depicts the correct relation between set A and B ?

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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