For a, b >0, let f(x)= {(tan (( a +1) x)+ b tan x)/x, x<0; 3, x=0; (√(a x+ b^2 x^2)-√(a x))/(b √ a x √ x), x>0} be a continous function at x=0. Then…

For $\displaystyle \mathrm{a}, \mathrm{b}>0$, let $\displaystyle f(x)= \begin{cases}\frac{\tan ((\mathrm{a}+1) x)+\mathrm{b} \tan x}{x}, & x<0 \\ 3, & x=0 \\ \frac{\sqrt{\mathrm{a} x+\mathrm{b}^2 x^2}-\sqrt{\mathrm{a} x}}{\mathrm{~b} \sqrt{\mathrm{a}} x \sqrt{x}}, & x>0\end{cases}$ be a continous function at $\displaystyle x=0$. Then $\displaystyle \frac{\mathrm{b}}{\mathrm{a}}$ is equal to: