1.
If the function
f(x)={1xloge(1+xa1xb),x<0k,x=0cos2xsin2x1x2+11,x>0f(x) = \begin{cases} \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{cases}

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