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Question Number 109722 by bemath last updated on 25/Aug/20

$$⊸\frac{\mathrm{♭}ϵ}{math}⊸$$$$\underset{x\to 0}{\lim }\frac{\sin x}{\sqrt{1-\cos x}}=?$$

Commented by bemath last updated on 25/Aug/20

Answered by mathmax by abdo last updated on 25/Aug/20

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{sinx}}{\sqrt{1-\mathrm{cosx}}}\mathrm{we}\mathrm{have}1-\mathrm{cosx}\sim \frac{{\mathrm{x}}^2}{2}\Rightarrow \sqrt{1-\mathrm{cosx}}\sim \frac{\mathrm{x}}{\sqrt{2}}$$$$\mathrm{akso}\mathrm{sinx}\sim \mathrm{x}\Rightarrow \mathrm{f}\left(\mathrm{x}\right)\sim \frac{\mathrm{x}}{\frac{\mathrm{x}}{\sqrt{2}}}=\sqrt{2}\Rightarrow {\lim }_{\mathrm{x}\to 0}\mathrm{f}\left(\mathrm{x}\right)=\sqrt{2}$$

Answered by mathmax by abdo last updated on 25/Aug/20

$$\mathrm{here}\mathrm{x}\to 0^{+}$$

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