_ x /2 [ x x - ( 2 ) x ] = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to \pi /2} \left[ {x\tan x - \left( {\frac{\pi }{2}} \right)\sec x} \right] = $

A
$1$
✓
$-1$
C
$0$
D
None of these

✓

Answer

Correct option: B.

$-1$

b
(b) $\mathop {\lim }\limits_{x \to \pi /2} \,\left[ {x\tan x - \left( {\frac{\pi }{2}} \right)\,\sec x} \right]$

$ = \mathop {\lim }\limits_{x \to \pi /2} \,\,\frac{{2x\,\,\sin x - \pi }}{{2\,\cos x}}$, $\left[ {{\rm{form}} \,\, \frac{0}{0}} \right]$

$ = \mathop {\lim }\limits_{x \to \pi /2} \,\,\frac{{[2\,\sin x + 2x\cos x]}}{{ - 2\,\sin x}} = - 1$, (By $L -$ Hospital’s rule).

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