From $5\mathrm{.}320$

$9.$ Given that $\frac{1}{1-x}={\displaystyle \underset{n=0}{\overset{}{}}}{x}^n$ with convergence in $(-1,1),$ find the power series for $g(x)=\frac{1}{1-2x^2}$ centred at $x=0$ and identify the interval of convergence.

From $6\mathrm{.}40$

$10.$ Find the Taylor series for the function $f(x)=sinx$ centred at $x=\frac{}{2}.$