1. If $P$ and $Q$ are polynomial functions with no common factors, then $y = Q(x)/P(x)$ is analytic at $x_0$ if and only if $P(x_0) \not= 0$. Moreover the radius of convergence of the power series for $ Q(x)/P(x) $ about the point $x_0$ is

$min\{||x_0 - x|| ~|~ x \in {\bf C}, P(x) = 0\}$

where $||x_0-x||$ = distance from $x_0$ to $x$ in the complex plane.

               A) True                        

2. The radius of convergence of the power series for $f(x) = {x \over (x^2 + 1)(x + 2)}$ about the point $x_0 = {1 \over 4}$ is $\geq \sqrt{({1 \over 4})^2 + (\pm 1)^2} = {\sqrt{17} \over 4}$

               A) True                        

3.) ${x \over (x^2 + 1)(x + 2)}$ $= \Sigma_{n=0}^\infty a_n(x - {1 \over 4})^n$ where $a_n = {f^{(n)}( {1 \over 4}) \over n!}$ for all values of $x \in ({1 - \sqrt{17} \over 4}, {1 + \sqrt{17} \over 4})$.

               A) True                        

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