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

If the function $\mathrm{f}\left(\mathrm{x}\right)=\frac{{\mathrm{cosec}}^2\mathrm{x}-2}{\mathrm{cotx}-1};\mathrm{x}=\frac{\mathrm{\pi }}{4}$ is continuous at $x=\frac{\mathrm{\pi }}{4}$, then the value of $f\left(\frac{\mathrm{\pi }}{4}\right)$ is

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

The number of points of discontinuities of $f\left(x\right)=\frac{x^2+4}{4x-x^3}$ is 

If $f\left(x\right)=\frac{x^2-1}{x^3+1},x\ne -1$ is continuous at $x=-1$, then the value of $f\left(-1\right)$ is 

If $f\left(x\right)=\frac{x^2-4}{x-2},x\ne 2$ is known to be continuous at $x=2$, then $f\left(2\right)$ is 

The function $f\left(x\right)=\left\{\begin{array}{l}\frac{\sin 3x}{x} , x\ne 0\\ \frac{k}{2} , x=0\end{array}\right.$is continuous at $x=0$; then $k$ is equal to