Embibe Experts Solutions for Chapter: Continuity & Derivability, Exercise 1: EXERCISE

If $f\left(x\right)=\left\{\begin{array}{ll}{x}^a\sin \left(\frac{1}{x}\right),& x\ne 0\\ 0,& x=0\end{array}\right.$ is continuous but non-differentiable at $x=0,$ then

If $f\left(x\right)=\left\{\begin{array}{ll}\sin x,& x<0\\ \cos x-\left|x-1\right|,& x\ge 0\end{array},\right.$ then $g\left(x\right)=f\left(\left|x\right|\right)$ is non-differentiable for

If $f\left(x\right)=\left\{\begin{array}{ll}{x}^2-ax+3,& x \text{is rational} \\ 2-x,& x \text{is irrational }\end{array}\right.$ is continuous at exactly two points, then the possible values of $\text{'}a\text{'}$ are

If $f\left(x\right)=\sqrt{1-\sqrt{1-x^2}},$ then $f\left(x\right)$ is

Let $y=f\left(x\right)=\left\{\begin{array}{cl}{e}^{-\frac{1}{x^2}}& \text{if} x\ne 0\\ 0& \text{if} x=0\end{array}\right.$. Then which of the following can best represent the graph of $y=f\left(x\right)$ ?

If $f\left(2+x\right)=f\left(-x\right)$ for all $x\in R,$ then differentiability at $x=4$ implies differentiability at

If both $f\left(x\right)$ and $g\left(x\right)$ are differentiable functions at $x=x_0$, then the function defined as $h\left(x\right)=$maximum $\left\{f\left(x\right), g\left(x\right)\right\}$

Let $f\left(x\right)=\underset{n\to \infty }{\lim }\frac{{\left(x^2+2x+3+\sin \pi x\right)}^n-1}{{\left(x^2+2x+3+\sin \pi x\right)}^n+1}$, then