MCQ_SINGLE

If \(f(x)=\begin{cases}\frac{\sin^{2}ax}{x^{2}},&x\ne0\\ 1,&x=0\end{cases}\) is continuous at \(x=0\), then the value of a is:

VSA

If $y=x^{\frac{1}{x}}$ then find $\frac{dy}{dx}$ at $x=1$.

SA

Find k so that $f(x)=\begin{cases}\frac{x^{2}-2x-3}{x+1},&x\ne-1\\ k,&x=-1\end{cases}$ is continuous at $x=-1$.

MCQ_SINGLE

The function f(x)=[x], where [x] denotes the greatest integer less than or equal to x, is continuous at

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 ?

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