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Question Number 193461 by SAMIRA last updated on 14/Jun/23

$$\underset{x\to 0}{\lim }\left(\frac{\sqrt{1+\sin \mathrm{x}}-1}{\sin 2\mathrm{x}}\right)=??$$

Answered by aba last updated on 14/Jun/23

$$=\underset{x\to 0}{\lim }\frac{1+\mathrm{sinx}-1}{\sin \left(2\mathrm{x}\right)(\sqrt{1+\mathrm{sinx}}+1)}=\underset{x\to 0}{\lim }\frac{1}{2\mathrm{cosx}(\sqrt{1+\mathrm{sinx}}+1)}=\frac{1}{4}✓$$

Answered by MM42 last updated on 14/Jun/23

$${lim}_{x\to 0}\left(\frac{sinx}{sin2x(\sqrt{1+sinx}+1)}\right)=\frac{1}{4}$$

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