Mathematics - Continuity - Differentiability Question with Solution | TestHub

The function $\mathrm{u}=\frac{1}{\mathrm{x}-1}$ is discontinuous at $\mathrm{x}=1$

$\mathrm{f}(\mathrm{x})=\frac{1}{(\mathrm{u}+1)(\mathrm{u}-2)}$ is discontinuous at $\mathrm{u}=-1,2$

i.e. at $x=0,\frac{3}{2}$

also we have ${\mathrm{Lt}}_{\mathrm{x}\to 0}\mathrm{f}(\mathrm{x})={\mathrm{Lt}}_{\mathrm{u}\to -1}\mathrm{f}(\mathrm{x})=\infty$

$$\begin{array}{rlr}& {\mathrm{Lt}}_{x\to \frac{3}{2}}f(x)={\mathrm{Lt}}_{u\to 2}f(x)=\infty & \end{array}$$

$${\mathrm{Lt}}_{x\to 1}f(x)={\mathrm{Lt}}_{x\to \infty }f(x)=0$$