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Question Number 100027 by bemath last updated on 24/Jun/20

$$\underset{x\to 0}{\lim }\mathrm{xsin}\left(\frac{1}{\mathrm{x}}\right)?$$

Commented by john santu last updated on 24/Jun/20

$$\underset{x\to 0}{\lim }\mathrm{x}=0\mathrm{\&}-1⩽\sin \left(\frac{1}{\mathrm{x}}\right)⩽1$$$$\mathrm{then}\underset{x\to 0}{\lim x}\sin \left(\frac{1}{\mathrm{x}}\right)=0◼$$

Commented by bobhans last updated on 24/Jun/20

$$\mathrm{yes}\mathrm{correct}.\lim =0$$

Answered by mathmax by abdo last updated on 24/Jun/20

$$\mid \mathrm{xsin}\left(\frac{1}{\mathrm{x}}\right)\mid ⩽\mid \mathrm{x}\mid \Rightarrow {\lim }_{\mathrm{x}\to 0}\mathrm{xsin}\left(\frac{1}{\mathrm{x}}\right)=0$$

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