Mathematics - Continuity - Differentiability Question with Solution | TestHub

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