JEE Main 2024 · Mathematics · Limits · easy

Lim x→0(1-cos 4x)/(x^2 equals

Single correct option

\displaystyle\lim_{x\to0}\dfrac{1-\cos4x}{x^2}

equals

Show answer and solution

Answer: (B) $8$

Use

1-\cos\theta=2\sin^2(\theta/2)

1-\cos4x=2\sin^2 2x

. Then the limit is

2\cdot\lim\dfrac{\sin^22x}{x^2}=2\cdot 4=8

. Alternatively

1-\cos kx\approx k^2x^2/2

gives

16/2=8

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