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Question Number 152362 by Tawa11 last updated on 27/Aug/21

$$\mathrm{f}\left(\mathrm{x}\right)=\{\begin{array}{l}\mathrm{x}\sin \frac{1}{\mathrm{x}},\mathrm{if}0<\mathrm{x}⩽1\\ 0,\mathrm{if}\mathrm{x}=0\end{array}$$ $$\mathrm{Show}\mathrm{that}\mathrm{f}\mathrm{is}\mathrm{continous}\mathrm{but}\mathrm{not}\mathrm{of}\mathrm{bounded}\mathrm{variation}$$

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