X -4lim-2-sec-2 x f-t-dt-x-2 - -2-16equals8-f-2-2-f-1-2-4f-2-2-f-2-

The correct option is A 8/πf(2)Required limits is of the form 0/0, so it is equal to x →π/4lim2 secx secx tan xf(sec^2 x)/2x= x →π/4limsec^2 x tanx f(sec^2 x)/ ...

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Byju's Answer

Standard XII

Mathematics

Property 5

x →π/4lim∫_2^...

Question

$l i m x \to \frac{π}{4} \frac{\int_{2}^{s e c^{2} x} f (t) d t}{x^{2} - \frac{π^{2}}{16}}$ equals

\frac{8}{π} f (2)

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\frac{2}{π} f (2)

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\frac{2}{π} f (\frac{1}{2})

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4 f (2)

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Solution

The correct option is A $\frac{8}{π} f (2)$
Required limits is of the form $\frac{0}{0}$ , so it is equal to
$l i m x \to \frac{π}{4} \frac{2 s e c x s e c x t a n x f (s e c^{2} x)}{2 x} = l i m x \to \frac{π}{4} \frac{s e c^{2} x t a n x f (s e c^{2} x)}{x} = \frac{8}{π} f (2)$

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limx→π4∫sec2x2f(t)dtx2−π216equals

The correct option is A 8πf(2)Required limits is of the form 00, so it is equal to limx→π42 secx secx tan xf(sec2x)2x=limx→π4sec2x tanx f(sec2x)x=8πf(2)

$l i m x \to \frac{π}{4} \frac{\int_{2}^{s e c^{2} x} f (t) d t}{x^{2} - \frac{π^{2}}{16}}$ equals

The correct option is A $\frac{8}{π} f (2)$
Required limits is of the form $\frac{0}{0}$ , so it is equal to
$l i m x \to \frac{π}{4} \frac{2 s e c x s e c x t a n x f (s e c^{2} x)}{2 x} = l i m x \to \frac{π}{4} \frac{s e c^{2} x t a n x f (s e c^{2} x)}{x} = \frac{8}{π} f (2)$