Q$1($a$)($i$)$ Find the first three non$-$zero terms of the Taylor's series for the function $f(x)=e^{1-8x}$ centered at $x=3.$

$($ii$)$ Use it to approximate the value of $e^9.$

$($b$)$ The region bounded by the curve $y=x^2-2,y=2-x^2,$ and $x=0$ in the second and third quadrant is revolved about the $y-$axis to generate a solid. Find the volume of the solid using the Shell Method.