Question:medium
If \(f(x) = \cot^{-1}\left(\frac{3x - x^3}{1 - 3x^2}\right)\) and \(g(x) = \cos^{-1}\left(\frac{1 - x^2}{1 + x^2}\right)\), then \(\lim_{x \to a} \frac{f(x) - f(a)}{g(x) - g(a)}\), \(0<a<1/2\), is
If \(f(x) = \cot^{-1}\left(\frac{3x - x^3}{1 - 3x^2}\right)\) and \(g(x) = \cos^{-1}\left(\frac{1 - x^2}{1 + x^2}\right)\), then \(\lim_{x \to a} \frac{f(x) - f(a)}{g(x) - g(a)}\), \(0<a<1/2\), is
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\(\cot^{-1}(\tan\theta) = \pi/2 - \theta\); \(\cos^{-1}(\cos 2\theta) = 2\theta\) for appropriate range.
Updated On: Apr 7, 2026
- \(\frac{3}{2(1 + a^2)}\)
- \(\frac{3}{2(1 + x^2)}\)
- \(\frac{3}{2}\)
- \(-\frac{3}{2}\)
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The Correct Option is D
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