question a

1. Consider partition a = x0

= b with equal spacing. Let W (X) be a piecewise quadratic 1. Consider partition a = < XI < Xn function such that W (C) w t (C) for .Til < < mi +1, i = n, and W i (c)is a quadratic polynomial satisfying conditions: ) = f (Ci-1) 3) Qt f (aYi) where a:'i is the midpoint of [Ci_l , a) Give an explicit formula for Wi (x) b) If f (c) is continuous, determine if W (x) is continuous on [a, b]. Justify. c) Show that the absolute value of the error of approximation of f (c) by W (C) on [a, b]does not exceed M(3) (Ax)3 , where M(3) is as defined in class. 720 3c3 e [O, l], determine what Ax (the partition radius under equidistant partition) d) If f (c) 24e should be so that the absolute value of the error of approximation of f (c) by W (C) does not exceed 10 4