Question Number 124995 by liberty last updated on 07/Dec/20
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}+\mathrm{sin}\:{x}}\:−\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}}{\mathrm{tan}\:{x}}\:=? \\ $$
Answered by bemath last updated on 07/Dec/20
Answered by Dwaipayan Shikari last updated on 07/Dec/20
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{2}}\left(\mathrm{1}+\frac{{x}}{\:\mathrm{4}}\right)−\sqrt{\mathrm{2}}}{{x}}=\sqrt{\mathrm{2}}\left(\frac{{x}}{\mathrm{4}{x}}\right)=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$