Reference no: EM131569016
1. Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on each interval.
a. [0,1] b. [1, 3.2] c. [3.2, 4]
2. Let f (x) = (x + 2)(x + 1)2x(x -1)3(x - 2). To which zero of f does the Bisection method converge when applied on the following intervals?
a. [-1.5, 2.5] b. [ -0.5, 2.4] c. [-0.5, 3] d. [-3, -0.5]
3. Use Theorem 2.1 to find a bound for the number of iterations needed to achieve an approximation with accuracy 10-3 to the solution of x3 + x - 4 = 0 lying in the interval [1, 4]. Find an approximation to the root with this degree of accuracy.
4. Let f (x) = (x - 1)10, p = 1, and pn = 1 + 1/n. Show that |(f(pn)| < 10-3 whenever n > 1 but that |p - pn| < 10-3 requires that n > 1000.