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Single Point Continuity

limx→∞ x cos ...

Question

$lim x \to \infty x cos (\frac{π}{8 x}) sin (\frac{π}{8 x}) =$

A

π

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B

\frac{π}{2}

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C

\frac{π}{8}

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D

\frac{π}{4}

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Solution

The correct option is C $\frac{π}{8}$
$lim x \to \infty \frac{x \cdot 2 sin (\frac{π}{8 x}) cos (\frac{π}{8 x})}{2}$
$= lim x \to \infty \frac{x \cdot sin (\frac{π}{4 x})}{2} = \frac{(\frac{π}{4})}{2} = \frac{π}{8}$

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Single Point Continuity

Standard XII Mathematics

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