Limx- x cos -8x sin -8x -

Name: JEE- Grade 12- Mathematics- Limits- Session 05- W04
Uploaded: 2022-07-04T10:36:42+05:30
Description: Lim_x→∞x· 2 sin ( π8x ) cos ( π8x )2 =lim_x→∞x·sin ( π4x )2= ( π4 )2= π8 ...

Lim_x→∞x· 2 sin ( π8x ) cos ( π8x )2 =lim_x→∞x·sin ( π4x )2= ( π4 )2= π8 ...

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Byju's Answer

Standard XII

Mathematics

Single Point Continuity

limx→∞ x cos ...

Question

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

π

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\frac{π}{2}

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\frac{π}{8}

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\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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limx→∞xcos(π8x)sin(π8x)=

The correct option is C π8limx→∞x⋅2sin(π8x)cos(π8x)2 =limx→∞x⋅sin(π4x)2=(π4)2=π8

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

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