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STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
$\mathop {\lim }\limits_{x \to 0} {\left\{ {\tan \left( {\frac{\pi }{4} + x} \right)} \right\}^{1/x}} = $
  • A
    $1$
  • B
    $-1$
  • ✓
    ${e^2}$
  • D
    $e$
✓

Answer

Correct option: C.
${e^2}$
c
(c) Given limit $ = \mathop {\lim }\limits_{x \to 0} \,\,{\left( {\frac{{1 + \tan x}}{{1 - \tan x}}} \right)^{1/x}}$

$ = \mathop {\lim }\limits_{x \to 0} \,\,\frac{{{{\{ {{(1 + \tan x)}^{1/\tan x}}\} }^{(\tan x)/x}}}}{{{{\{ {{(1 - \tan x)}^{1/\tan x}}\} }^{(\tan x)/x}}}} = \frac{e}{{{e^{ - 1}}}} = {e^2}$.

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