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Question Number 91897 by john santu last updated on 03/May/20

$$\underset{x\to 0}{\lim }\frac{\sin (2x-\sin x)}{1-\sqrt{1-x^2}}=?$$

Commented by john santu last updated on 03/May/20

$$\underset{x\to 0}{\lim }\frac{2x-\sin x}{1-(1-\frac{x^2}{2})}=$$$$\underset{x\to 0}{\lim }\frac{2x-(x-\frac{x^3}{6})}{\frac{x^2}{2}}=$$$$\underset{x\to 0}{\lim }\frac{2(x+\frac{x^3}{6})}{x^2}=$$$$\underset{x\to 0}{\lim }\frac{2}{x}+\frac{x}{3}=D\mathrm{NE}$$

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