JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If the function \(f(x)=\frac{\cos (\sin x)-\cos x}{x^{4}}\) is continuous at each point in its domain and \(f (0)=\frac{1}{ k },\) then \(k\) is ........
- A \(6\)
- B \(8\)
- C \(10\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{\cos (\sin x)-\cos x}{x^{4}}=f(0)\) \(\Rightarrow \lim _{x \rightarrow 0} \frac{2 \sin \left(\frac{\sin x+x}{2}\right) \sin \left(\frac{x-\sin x}{2}\right)}{x^{4}}=\frac{1}{K}\)…
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