Mathematics - Continuity - Differentiability Question with Solution | TestHub

$1=f(0)={\mathrm{Lim}}_{x\to 0}f(x)={\mathrm{Lim}}_{x\to 0}\frac{x(1+a\left(1-\frac{x^2}{\lfloor 2}+\dots \right)-b(x-\frac{x^3}{\lfloor 3}+\dots .}{x^3}$ $={\mathrm{Lim}}_{x\to 0}\frac{x(1+a-b)+x^3\left(\frac{-a}{2}+\frac{b}{6}\right)+x^5(\lambda )+\dots \dots ..}{x^3}$ $\Rightarrow 1+a-b=0$ and $\frac{-a}{2}+\frac{b}{6}=1\Rightarrow a=\frac{-5}{2},b=\frac{-3}{2}$ and $2a-8b=7$