If the function $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\frac{1}{x} \log _e\left(\frac{1+\frac{a}{x}}{1-\frac{x}{b}}\right) & , x<0 \\ k & , x=0 \\ \frac{\cos ^2 x-\sin ^2 x-1}{\sqrt{x^2+1}-1} & , x>0\end{array}\right.$
Is continuous at $\mathrm{x}=0$, then $\frac{1}{a}+\frac{1}{b}+\frac{4}{k}$ is equal to :