A) 1
B) e
C) \[{{e}^{2}}\]
D) \[\sqrt{e}\]
Correct Answer: C
Solution :
[c] : \[\exp \underset{x\to 0}{\mathop{\lim }}\,\frac{\tan \left( \frac{\pi }{4}+x \right)-1}{x}\] \[=\exp \underset{x\to 0}{\mathop{\lim }}\,\left( \frac{1+\tan x}{1-\tan x}-1 \right)\frac{1}{x}\] \[=\exp \underset{x\to 0}{\mathop{\lim }}\,\frac{2\tan x}{x}\frac{1}{(1-\tan x)}={{e}^{2}}\]You need to login to perform this action.
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