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Question Number 12881 by kunalshukla95040 last updated on 05/May/17

$$\frac{lim}{x\to 0}\frac{\sqrt{1-\cos x}}{x}$$$$isequalsto.$$

Answered by nume1114 last updated on 05/May/17

$$\underset{x\to 0}{\lim }\frac{\sqrt{1-\cos x}}{x}$$$$=\underset{x\to 0}{\lim }\frac{\sqrt{1-(1-{2\sin }^2\left(\frac{x}{2}\right))}}{x}$$$$=\underset{x\to 0}{\lim }\frac{\sqrt{2}\sin \left(\frac{x}{2}\right)}{2\cdot \frac{x}{2}}$$$$=\frac{\sqrt{2}}{2}\underset{x\to 0}{\lim }\frac{\sin \left(\frac{x}{2}\right)}{\frac{x}{2}}$$$$=\frac{\sqrt{2}}{2}\left(or\frac{1}{\sqrt{2}}\right)$$

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