$lim x \to \frac{π}{2} \frac{[\frac{x}{2}]}{log sin x}$ , where $[.]$ denotes the greatest integer function, is:

1

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0

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Solution

The correct option is A $0$
We know, $1 < \frac{π}{2} < 2$
$\Rightarrow lim x \to \frac{π}{2} [\frac{x}{2}] = 0$
Thus,
$lim x \to \frac{π}{2} \frac{[\frac{x}{2}]}{log sin x} = \frac{0}{log (A real number close to 1 but not equal to 1)} = 0$

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