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In-Class Exercises

In each of the following problems, find the zeros of the following functions
over the interval [0, 5].
2
Pb. 5.6 f(x) = x + 1. (Alert: Applying fsolve blindly could lead you into
trouble!)
2
Pb. 5.7 f(x) = sin (x) – 1/2. Compare your answer with the analytical result.
2
Pb. 5.8 f(x) = 2 sin (x) – x 2
Pb. 5.9 f(x) = x – tan(x)

Zeros of a Function in Two Variables
As previously noted, the power of the MATLAB fsolve function really
shines in evaluating the roots of multivariable functions.

Example 5.3
Find the intersection in the x-y plane of the parabaloid and the plane given in
Pb. 5.1.

Solution: We follow these steps:

1. Use the contour command to estimate the coordinates of the
points of intersection of the surfaces in the x-y plane.
2. Construct the function M-file for two functions (z , z ) having two
1 2
inputs (x, y):

function farray=funname(array)
x=array(1);
y=array(2);
farray(1)=7-sqrt(25+x.^2+y.^2);
farray(2)=4-2*x-4*y;

3. Use the approximate value found in step 1 as the value for the
guess array; for example:

xyguess=[4 -1];

4. Finally, use the fsolve command to accurately find the root. The
syntax is:

© 2001 by CRC Press LLC