Consider the functions y D. For y A. Write the Taylor expansions for the two functions about x = 0. What is similar about the two series? What is different? 1 1+x' B. Looking at the series, which function do you predict will be greater over the interval (1,1)? 1 1+x and y = 1 sin(x). the radius of convergence is R = C. Are these functions even or odd? E. For y = 1 - sin(x), the radius of convergence is R - (type inf if the radius of convergence is infinite to get ). (type inf if the radius of convergence is infinite to get ). Looking at the relative sizes of the successive terms in your series, note how the radii of convergence you found make sense.