If the function f(x)= {1/x log_e ((1+x/a)/(1-x/b)), x<0; k, x=0; (cos^2 x- sin^2 x-1)/(√(x^2+1)-1), x>0} is continuous at x=0, then 1/a+1/b+4/k is…

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