Mathematics - Continuity - Differentiability Question with Solution | TestHub

$f(x)=00<x<1$

$$=\sin \pi x1\le x<\sqrt{2}=2$$

$$\sin \pi x\sqrt{2}\le x<\sqrt{3}=3$$

$$\sin \pi x\sqrt{3}\le x<2=4$$

$$\sin \pi x2\le x<\sqrt{5}etc.$$

The function is discontinuous at $\mathrm{x}=\sqrt{2},\sqrt{3},\sqrt{5},\dots \dots \sqrt{\mathrm{K}}$ where K is not a perfect square.

Points of discontinuity $($ desired $)=\sqrt{2},\sqrt{3},\sqrt{5},\sqrt{6},\sqrt{7},\sqrt{8}$