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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 Spring '08
 Chelikowsky
 Chemical Engineering, #, 2 Pt, Rootfinding algorithm

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