COMEDK · Maths · 16. Limits
\(\lim\limits_{x \to 0}\dfrac{(1 - \cos 2x)(3 + \cos x)}{x\tan 4x}\) is equal to:
- A \(1\)
- B \(4\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\lim\limits_{x \to 0}\dfrac{(1 - \cos 2x)(3 + \cos x)}{x\tan 4x}\) Using the trigonometric identity \(1 - \cos 2x = 2\sin^2 x\): \(= \lim\limits_{x \to 0}\dfrac{2\sin^2 x(3 + \cos x)}{x\tan 4x}\) Dividing the numerator and the denominator by \(x^2\):…
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