(a) Verify whether the function $f$ defined by $f(x)=\left\{\begin{array}{cl}x \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$ is continuous at $x=0$ or not.

OR

(b) Check for differentiability of the function $f$ defined by $f(x)=|x-5|$, at the point $x=5$.

The area of the circle is increasing at a uniform rate of $2 \mathrm{~cm}^2 / \mathrm{s}$. How fast is the circumference of the circle increasing when the radius $r=5 \mathrm{~cm}$ ?

(a) Find: $\int \cos ^3 x e^{\log \sin x} d x$

OR

(b) Find: $\int \frac{1}{5+4 x-x^2} d x$

Find the vector equation of the line passing through the point $(2,3,-5)$ and making equal angles with the co-ordinate axes.