If the function f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩1xloge⎛⎜⎜⎝1+xa1−xb⎞⎟⎟⎠,x<0k,x=0cos2x−sin2x−1√x2+1−1,x>0is continuous at x=0, then 1a+1b+4k is equal to:

If the function f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪�

1.	If the function f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩1xloge⎛⎜⎜⎝1+xa1−xb⎞⎟⎟⎠,x<0k,x=0cos2x−sin2x−1√x2+1−1,x>0is continuous at x=0, then 1a+1b+4k is equal to:
Answer» If the function $f (x) = ⎧ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ ⎩ \begin{matrix} \frac{1}{x} {log}_{e} ⎛ ⎜⎜ ⎝ \frac{1 + \frac{x}{a}}{1 - \frac{x}{b}} ⎞ ⎟⎟ ⎠, & x < 0 k, & x = 0 \frac{{cos}^{2} x - {sin}^{2} x - 1}{\sqrt{x^{2} + 1} - 1}, & x > 0 \end{matrix}$ is continuous at $x = 0,$ then $\frac{1}{a} + \frac{1}{b} + \frac{4}{k}$ is equal to: