R D Sharma Solutions for Chapter: Differentiability, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

If $f\left(x\right)=\sqrt{x^2+9}$, write the value of $\underset{x\to 4}{\lim }\frac{f\left(x\right)-f\left(4\right)}{x-4}$.

The function $f\left(x\right)=\frac{\sin \left(\pi \right[x-\pi \left]\right)}{4+[x{]}^2}$, where $\left[·\right]$ denotes the greatest integer function, is

Let $f\left(x\right)=a+b\left|x\right|+c|x{|}^4$, where $a, b$ and $c$ are real constants. Then, $f\left(x\right)$ is differentiable at $x=0$, if

If $f\left(x\right)=|3-x|+(3+x)$, where $\left(x\right)$ denotes the least integer greater than or equal to $x$, then $f\left(x\right)$ is

If $f\left(x\right)=\left\{\begin{array}{cc}\frac{1}{1+e^{{\displaystyle \frac{1}{x}}}},& x\ne 0\\ 0,& x=0\end{array}\right.$, then $f\left(x\right)$ is

If $f\left(x\right)=\left\{\begin{array}{ll}\frac{1-\cos x}{x\sin x},& x\ne 0\\ \frac{1}{2},& x=0\end{array}\right.$, then at $x=0, f\left(x\right)$ is

The set of points where the function $f\left(x\right)$ given by $f\left(x\right)=|x-3| \cos x$ is differentiable, is

Let $f\left(x\right)=\left\{\begin{array}{rrr}1& ,& x\le -1\\ \left|x\right|& ,& -1<x<1\\ 0& ,& x\ge 1\end{array}\right.$. Then $f$ is