Page 81 - Numerical Analysis Using MATLAB and Excel

Chapter 2 Root Approximations

2.5 Exercises

1. Use MATLAB to sketch the graph y = f x() for each of the following functions, and verify
from the graph that fa() and fb() , where and defined below, have opposite signs. Then,
a
b
use Newton’s method to estimate the root of fx() = 0 that lies between and . b
a
4
a. f x() = x + x3 a = 1 b = 2
–
1
b. f x() = 2x + 1 – x + 4 a = 2 b = 4
2
)
Hint: Start with x = ( a + b ⁄ 2
0
2. Repeat Exercise 1 above using the Bisection method.

3. Repeat Example 2.5 using MATLAB.
Hint: Use the procedure of Example 2.2

2−28 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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