Written Assignment $4$

Give complete solutions for each problem showing all $of$ your work.

Find the interval $of$ convergence for the series ${\displaystyle \underset{n=0}{\overset{}{}}}\frac{(x-7{)}^{2n}}{{25}^n}.$

Find the Taylor series centered $atx=2$ for $f(x)=\frac{1}{10-x}.$

Find a parametric expression for the line segment with endpoints $(-8,-7)$ and

$(0,-12).$

Find the Cartesian coordinates for the polar coordinate point $(\sqrt[\phantom{2}]{3},\frac{}{6}).$

Find the area inside the circle $r=\sqrt[\phantom{2}]{3}sinand$ outside the cardioid $r=1+cos.$