If $f(x)=\cot^{-1}\big[\large\frac{3x-x^3}{1-3x^2}\big]$ and $g(x)=\cos^{-1}\big[\large\frac{1-x^2}{1+x^2}\big]$ then $\lim\limits_{x\to a}\large\frac{f(x)-f(a)}{g(x)-g(a)}$$\quad0 < a < \large\frac{1}{2}$ is

Question

$\begin{array}{1 1}(a)\;\large\frac{3}{2}&(b)\;\large\frac{3}{2(1+x^2)}\\(c)\;-\large\frac{3}{2}&(d)\;\large\frac{3}{2(1+a^2)}\end{array}$