Embibe Experts Solutions for Chapter: Continuity and Differentiability, Exercise 1: Exercise

Consider the function $f\left(x\right)=\frac{1}{x+2}$, then $f$ is 

The relation between $a$ and $b$ so that the function $f\left(x\right)$ defined by $f\left(x\right)=\left\{\begin{array}{ll}ax+1& ,\text{ if }x\le 3\\ bx+3,& , \text{ if }x>3\end{array}\right.$ is continuous at $x=3$ is

The value of $f \left(0\right),$ so that the function $f\left(x\right)=\frac{(27-2x{)}^{{\displaystyle \frac{1}{3}}}-3}{9-3(243+5x{)}^{{\displaystyle \frac{1}{5}}}}\left(x\ne 0\right)$ is continuous, is given by 

The value of $f \left(0\right),$ so that the function $f\left(x\right)=\frac{2-(256-7x{)}^{{\displaystyle \frac{1}{8}}}}{(5x+32{)}^{{\displaystyle \frac{1}{5}}}-2},x\ne 0$ is continuous, is given by 

If $f\left(x\right)=\left\{\begin{array}{cc}\frac{{36}^x-9^x-4^x+1}{\sqrt{2}-\sqrt{1+\cos x}},& \text{if} x\ne 0\\ k,& \text{if} x=0\end{array}\right.$ is continuous at $x=0,$ then $k$ equals

The function $f\left(x\right)$ is defined such that $f\left(x\right)=\frac{1}{x+2}$ and $g\left(x\right)=x^2+2x$, then derivative of $f\left(x\right)$ with respect to $g\left(x\right)$ at $x=1$  is

If $y^{\frac{1}{n}}+y^{-\frac{1}{n}}=2x,\text{ then find }\left(x^2-1\right)y_2+x{y}_1=$