HW_02-10-F

# HW_02-10-F - ChE 348 Homework 2_Due Thursday 16 September...

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ChE 348 Homework # 2 _________________________________________________Due: Thursday, 16 September 2010 Bisection Method 1. Do three steps (by hand) of the bisection method for f(x) = x 3 – e - x , using initial guesses of your choice. 2. Write a MATLAB script to use bisection to find a root of a general function f(x) on the interval a < x < b . Assume that there is one and only one simple root in this interval. Input parameters should be a , b and the maximum allowable error in the root. Verify the general program by finding the positive root of f(x) = x 3 – e - x . This function has one and only one simple root located at x = 0.77288. (Set the initial interval carefully.) Newton’s Method 3. Using Newton’s method, find the root of the following equation. (Do three iterations by hand with the given initial guesses, and write down corresponding errors). f(x) = x 2 – sin x , x 0 = 1/2 4. Write a MATLAB script to use Newton’s method to find a root of a general function f(x) . Assume that the method will converge to a root. Input parameters should be an initial guess

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HW_02-10-F - ChE 348 Homework 2_Due Thursday 16 September...

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