Categories > fun-lim > Limits > If $f(x)\,={{\cot }^{-1}}\left( \frac{3x-{{x}^{3}}}{1-3{{x}^{2}}} \right)$ and $g(x)={{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)$ , then $\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)-f(a)}{g(x)\,-g(a)},$ $0<\,a < \frac{1}{2}$ is

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Question: If $f(x)\,={{\cot }^{-1}}\left( \frac{3x-{{x}^{3}}}{1-3{{x}^{2}}} \right)$ and $g(x)={{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)$ , then $\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)-f(a)}{g(x)\,-g(a)},$ $0<\,a < \frac{1}{2}$ is


1) $\frac{3}{2(1+{{a}^{2}})}$
2) $\frac{3}{2(1+{{x}^{2}})}$
3) $\frac{3}{2}$
4) $-\frac{3}{2}$
Solution: Explanation: No Explanation
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