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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 30

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,{{\left( \tan \left( \frac{\pi }{4}+x \right) \right)}^{1/x}}=\]

    A) 1                     

    B) e

    C) \[{{e}^{2}}\]                          

    D)  \[\sqrt{e}\]

    Correct Answer: C

    Solution :

    [c] : \[\exp \underset{x\to 0}{\mathop{\lim }}\,\frac{\tan \left( \frac{\pi }{4}+x \right)-1}{x}\] \[=\exp \underset{x\to 0}{\mathop{\lim }}\,\left( \frac{1+\tan x}{1-\tan x}-1 \right)\frac{1}{x}\] \[=\exp \underset{x\to 0}{\mathop{\lim }}\,\frac{2\tan x}{x}\frac{1}{(1-\tan x)}={{e}^{2}}\]


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