a$)$ Find a power series representation at $c=0$ for the function $f(x)=sin(x).$

b$)$ Using series from part a$)($or using a method of your choice$)$ find the power series representation at $c-0$ for:

$g(x)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{sinx}{x}dx$

c$)$ Use the result in b$)$ to estimate $g(x)={\displaystyle \underset{0}{\overset{\frac{sinx}{x}}{}}}dx$ with an error below $0\mathrm{.}0001.$