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Question Number 124995 by liberty last updated on 07/Dec/20

$$\underset{x\to 0}{\lim }\frac{\sqrt{2+\sin x}-\sqrt{1+\cos x}}{\tan x}=?$$

Answered by bemath last updated on 07/Dec/20

Answered by Dwaipayan Shikari last updated on 07/Dec/20

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

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