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Question Number 77533 by vishalbhardwaj last updated on 07/Jan/20

$$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\sin \left(\frac{1}{\mathrm{x}}\right)\mathrm{where}\mathrm{x}\ne 0$$$$\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{function}\mathrm{at}\mathrm{x}=0$$$$\mathrm{and}\mathrm{given}\mathrm{that}\mathrm{function}\mathrm{is}\mathrm{continuous}\mathrm{at}\mathrm{x}=0?$$

Answered by MJS last updated on 07/Jan/20

$$\underset{x\to 0}{\lim }x\sin \frac{1}{x}=$$$$[\mathrm{let}x=\frac{1}{t}]$$$$=\underset{t\to \pm \mathrm{\infty }}{\lim }\frac{\sin t}{t}=0$$$$\Rightarrow f\left(0\right)=0$$

Commented by vishalbhardwaj last updated on 07/Jan/20

thanks a lot sir

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