n

Maclaurin Series expansion of the arctangent function x is defined for |x| 1 as (-1)" 2n +1 arctan2= Start with the simplest version, arctan x = x, and add one order at a time to estimate arctan(r/23), arctan(r/7) and arctan(7/13). Calculate the percentage of true and approximate relative error as each new term is added Plot the order vs Ea graph, please take the log. (The error is less than 0.0001%) Plot the term vs & graph, please take the log. true_value-approximation x 100% true_value Log error Current approximation - Previous approximation Current approximation Try to draw the total error shown as below. -x2n+-1 Total error Point of diminishing returns Truncation error Round-off error Log step size x 100%