L00 0.75 The error function is defined by 0.50 0.25 2 erf(z) = Co.00 1. dt %3D -0.25 -0.50 for all values of x. -0.75 -1.00 There is no antiderivative of e-² formed from polynomial, root, exponential, logarithmic, trigonometric functions. Yet the crror function has significant uses in probability, statistics, and other ficlds; so computing accurate estimates is important. which is an elementary function, ie. one which can be (a) Use a Riemann sum with 4 subintervals to estimate the value erf(0.2). (b) By replacing e¯² with its degree four Taylor polynomial about a = 0 (which can be integrated), find another estimate for the value of erf(0.2). (c) Repeat parts (a) and (b) for the value erf(2) (d) Provide sketches for parts (a)-(c). For example, sketch Ricmann sums and regions bencath appropriate curves. (c) Are accurate cstimates obtained in parts (a)-(c)? Why or why not? What changes would result in more accurate estimates? (x)j10