Show that the function  is  continuous but not differentiable at x=3. 

Determine the value of the constant ‘k’ so that the function  is continuous at x = 0.

For what value of k is the following function continuous at x = 2?

$\mathrm{f} ( \mathrm{x} ) =\begin{array}{c}2\mathrm{x} + 1 ; \mathrm{x}<2\\ \mathrm{k} ; \mathrm{x} = 2\\ 3\mathrm{x} - 1 ; \mathrm{x}>1 \end{array}$

Differentiate the following function w.r.t. x:

y = ${\left(\mathrm{sinx}\right)}^{\mathrm{x}} + {\sin }^{-1}\sqrt{\mathrm{x}}$

Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ if (x² + y²)² = xy.

If y =3 cos ( log x ) + 4 sin ( log x ), then show that ${\mathrm{x}}^2 \frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + \mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{y} = 0$