The value of lim x → 0 1 - cos 2 x 3 + cos x x tan 4 x is equal to

Given lim x → 0 1 - cos 2 x 3 + cos x x tan 4 x = lim x → 0 2 sin 2 x 3 + cos x x tan 4 x = lim x → 0 sin x x 2 4 x tan 4 x 3 + cos x × 1 2 = 2

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Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsTrigonometric and Inverse Trigonometric limitsMedium2 minPYQ_2013

MathematicsMediumsingle choice

The value of $\lim_{x \to 0} \frac{(1 - \cos 2 x) (3 + \cos x)}{x \tan 4 x}$ is equal to

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Answer:

Solution:

Given $\lim_{x \to 0} \frac{(1 - \cos 2 x) (3 + \cos x)}{x \tan 4 x}$

$= \lim_{x \to 0} \frac{2 \sin^{2} x (3 + \cos x)}{x \tan 4 x}$

$= \lim_{x \to 0} {(\frac{\sin x}{x})}^{2} (\frac{4 x}{\tan 4 x}) (3 + \cos x) \times \frac{1}{2}$

$= 2$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Trigonometric and Inverse Trigonometric limits

⏱ 2mℹ️ Source: PYQ_2013

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