Solutions to selected exercises Use the Bisection method to nd solutions accurate to within 102 for x3 7x2 + 14x 6 = 0 on [0,1]. Solution: Let f (x) = x3 7x2 + 14x 6 = 0. Note that f (0) = 6 < 0 and f
Math 4650 Homework #3 Solutions 1.3 #7. Find the rates of convergence of the following functions as h 0. 1. lim sin h = 1. h0 h Use sin h = h
h3 6
+ , and we get
sin h h h3 h2 sin h 1= = + = + . h h
Math 4650 Homework #2 Solutions 1.2 #3ab. Suppose p must approximate p with relative error at most 103 . Find the largest interval in which p must lie for each value of p. Solution: The relative error
Math 4650 Homework #1 Solutions 1. 1.1 #2. Find intervals containing solutions to the following equations. Solution: For all of these problems, we need to use the intermediate value theorem. So we wan