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$\lim _{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right)$ is equal to
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2
We have,
$\lim _{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right)$
$=\lim _{x \rightarrow 0} \frac{(\tan x)(\sqrt{2 x+4}+2)}{(2 x+4)-4}$
$=\lim _{x \rightarrow 0} \frac{\tan x(\sqrt{2 x+4}+2)}{2 x}$
$=\frac{1}{2} \times(\sqrt{4}+2)=\frac{1}{2}(2+2)=2$
$\lim _{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right)$
$=\lim _{x \rightarrow 0} \frac{(\tan x)(\sqrt{2 x+4}+2)}{(2 x+4)-4}$
$=\lim _{x \rightarrow 0} \frac{\tan x(\sqrt{2 x+4}+2)}{2 x}$
$=\frac{1}{2} \times(\sqrt{4}+2)=\frac{1}{2}(2+2)=2$
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