Do question 5 only

Homework 2 MATH 451 Numerical Analysis I September 14, 2018 Due Date: Wednesday. September 26, 2018, before the class (10:20-11:10am). No home- work submissions will the accepted after the due date, Discussion is encouraged but you need to write out your solutions independently 1. (10 points) Use the Bisection method to find ps for f()Vi-coss on (0.1). 2 (20 points) Determine the number of iterations necessary to solve -2 with accuracy 10-5 on [0,1). 3. (10 points) Use algebraic manipulation to show that the following functions has a fixed point at p precisely when fu) = o, where f(z)-z" +2x2-3. 4. (20 points) For the following function g(r), show that the fixed point iteration will converge on the interval [3, 5]. Estimate the number of iterations needed to obtaitn approximations accurate to within 10-5. Use the initial guess po = 3. 3. t2 5. (20 points) Write a program (code) to compute the square root of m by bisection method when m- 7, 13. This means you need to find solution of the equation r2-m 0 when m 7,13. The interval [a, b should be chosen as [s, s +1], where s is an integer such that s