Using calculus, it can be shown that the arctangent function can be approximated by the polynomial arctan x ≈ - x3 / 3 + x5 / 5 - x7 / 7 where x is in radians.
(a) Use a graphing utility to graph the arctangent function and its polynomial approximation in
the same viewing window. How do the graphs compare?
(b) Study the pattern in the polynomial approximation of the arctangent function and predict the next term. Then repeat part (a). How does the accuracy of the approximation change when an additional term is added?