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Question Number 142721 by mathlove last updated on 04/Jun/21

$$\underset{x\to 0}{\lim }\frac{x}{\sqrt{1-\cos x}}=?$$

Answered by Ar Brandon last updated on 04/Jun/21

$$\underset{\mathrm{x}\to 0}{\lim }\frac{\mathrm{x}}{\sqrt{1-\mathrm{cosx}}}=\underset{\mathrm{x}\to 0}{\lim }\frac{\mathrm{x}}{\sqrt{1-(1-\frac{{\mathrm{x}}^2}{2})}}=\underset{\mathrm{x}\to 0}{\lim }\frac{\mathrm{x}}{\sqrt{{\mathrm{x}}^2/2}}=\frac{\mathrm{x}\sqrt{2}}{\pm \mathrm{x}}=\pm \sqrt{2}$$

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