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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
Let $p = \mathop {\lim }\limits_{x \to 0 + } {\left( {1 + {{\tan }^2}\sqrt x } \right)^{\frac{1}{{2x}}}},$ then $\log p = $ . . . 
  • ✓
    $\frac{1}{2}\;\;$
  • B
    $\frac{1}{4}$
  • C
    $2$
  • D
    $1$
✓

Answer

Correct option: A.
$\frac{1}{2}\;\;$
a
${\rm{p}} = {{\rm{e}}^{\mathop {\lim }\limits_{x \to {0^ + }} \frac{1}{2}{{\left( {\frac{{{\mathop{\rm san}\nolimits} \sqrt x }}{{\sqrt x }}} \right)}^2}}} = \sqrt e $

$\log p = \frac{1}{2}$

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