Consider the functions $y=1 - \ln(1+x^2)$ and $y={1\over1+x^2}$.

A. Write the Taylor expansions for the two functions about $x=0$. What is similar about the two series? What is different? Looking at the series, which function do you predict will be greater over the interval (-1,1)?
A. $1 - \ln(1+x^2)$
B. ${1\over1+x^2}$

(Graph the functions to verify that your answer is correct!)

B. Are these functions even or odd?
A. Even
B. Odd

C. Find the radii of convergence for your two series.
For $1 - \ln(1+x^2)$, the radius of convergence is
For ${1\over1+x^2}$, the radius of convergence is
(Enter infinity if the radius of convergence is infinite.)

Looking at the relative sizes of the successive terms in your series, note how the radii of convergence you found make sense.