JEE Mains · Maths · STD 11 - 12. limits
\(\lim\limits _{x \rightarrow 0} \frac{\cos (\sin x)-\cos x}{x^{4}}\) is equal to :
- A \(\frac{1}{3}\)
- B \(\frac{1}{4}\)
- C \(\frac{1}{6}\)
- D \(\frac{1}{12}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{6}\)
Step-by-step Solution
Detailed explanation
\(\lim\limits _{x \rightarrow 0} \frac{\cos (\sin x)-\cos x}{x^{4}} ;\left(\frac{0}{0}\right)\) \(\lim \limits_{x \rightarrow 0}\left(\frac{2 \cdot \sin \left(\frac{x+\sin x}{2}\right) \sin \left(\frac{x-\sin x}{2}\right)}{x^{4}}\right)\)…
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