Page 58 - A Guide to MATLAB for Beginners and Experienced Users

M-Files 39

% Define the vector of values of the independent variable
x = [0.1, 0.01, 0.001];

% Compute the desired values
y = sin(x)./x
% These values illustrate the fact that the limit of
% sin(x)/x as x approaches 0 is equal to 1.

echo off
Sometimes you may need to type, either in the Command Window or in an
M-file, a command that is too long to fit on one line. If so, when you get near
the end of a line you can type ... (that is, three successive periods) followed
by ENTER, and continue the command on the next line. In the Command
Window, you will not see a command prompt on the new line.

Function M-Files

You often need to repeat a process several times for different input values of a
parameter. For example, you can provide different inputs to a built-in function
to find an output that meets a given criterion. As you have already seen, you
can use inline to define your own functions. In many situations, however,
it is more convenient to define a function using an M-file instead of an inline
function.
Let us return to the problem described above, where we computed some
values of sin(x)/x with x = 10 −b for several values of b. Suppose, in addition,
−b
−b
that you want to find the smallest value of b for which sin(10 )/(10 ) and 1
agree to 15 digits. Here is a function M-file called sinelimit.m designed to
solve that problem:

function y = sinelimit(c)
% SINELIMIT computes sin(x)/x for x = 10ˆ(-b),
% whereb=1, ..., c.
format long
b = 1:c;
x = 10.ˆ(-b);
y = (sin(x)./x)’;
Like a script M-file, a function M-file is a plain text file that should reside in
your MATLAB working directory. The first line of the file contains a function