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Question Number 193458 by SAMIRA last updated on 14/Jun/23

$$\underset{x\to 0}{\lim }\left(\frac{1-\cos \left(\mathrm{x}\right)}{\mathrm{x}\sin \left(\mathrm{x}\right)}\right)=???$$

Commented by aba last updated on 14/Jun/23

$$\underset{\mathrm{x}\to 0}{\lim }\frac{1-\cos \left(\mathrm{x}\right)}{\mathrm{xsin}\left(\mathrm{x}\right)}=\underset{x\to 0}{\lim }\frac{1-\cos \left(\mathrm{x}\right)}{{\mathrm{x}}^2}\times \frac{\mathrm{x}}{\sin \left(\mathrm{x}\right)}=\frac{1}{2}\times 1=0.5$$

Answered by MM42 last updated on 14/Jun/23

$${lim}_{x\to 0}\frac{\frac{1}{2}{x}^2}{x^2}=\frac{1}{2}$$

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