If the function \(f(x)=\left\{\begin{array}{cc}\frac{1}{x} \log _e\left(\frac{1+\frac{x}{a}}{1-\frac{x}{b}}\right) & , x…

If the function \(f(x)=\left\{\begin{array}{cc}\frac{1}{x} \log _e\left(\frac{1+\frac{x}{a}}{1-\frac{x}{b}}\right) & , x<0 \\k & , x=0 \\\frac{\cos ^2 x-\sin ^2 x-1}{\sqrt{x^2+1}-1} & , x>0\end{array}\right.\)

is continuous at \(x =0\), then \(\frac{1}{a}+\frac{1}{b}+\frac{4}{k}\) s equal to:

[JEE Main 2021, 31 Aug (Shift 1)]