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Question Number 127846 by bemath last updated on 02/Jan/21

$$\underset{x\to 0}{\lim }\frac{{\mathrm{x}}^3\sin \left(\frac{1}{\mathrm{x}}\right)}{\sin {}^2\left(\mathrm{x}\right)}?$$

Commented by Dwaipayan Shikari last updated on 02/Jan/21

$$\underset{x\to 0}{\lim }\frac{xsin\left(\frac{1}{x}\right)}{{sin}^{2}x}=xsin\left(\frac{1}{x}\right)$$$$-1⩽sin\frac{1}{x}⩽1\Rightarrow \underset{x\to 0}{\lim }xsin\frac{1}{x}=0$$

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