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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 1} (1 - x)\tan \left( {\frac{{\pi x}}{2}} \right) = $
  • A
    $\frac{\pi }{2}$
  • B
    $\pi $
  • ✓
    $\frac{2}{\pi }$
  • D
    $0$
✓

Answer

Correct option: C.
$\frac{2}{\pi }$
c
(c) $\mathop {\lim }\limits_{x \to 1} \,(1 - x)\tan \,\left( {\frac{{\pi x}}{2}} \right)$.

Put $1 - x = y$ as $x \to 1,\,\,y \to 0$

Thus $\mathop {\lim }\limits_{y \to 0} \,\,y\tan \frac{{\pi \,(1 - y)}}{2} = \mathop {\lim }\limits_{y \to 0} \,\,\frac{2}{\pi }.\frac{{\left( {\frac{{\pi y}}{2}} \right)}}{{\tan \,\left( {\frac{{\pi y}}{2}} \right)}} $

$= \frac{2}{\pi } \times 1 = \frac{2}{\pi }$.

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