the equation f(x)=0, with f(x)=e^{-x^2}\sin(5x), in the interval [-1,1] has 1 real root 3 real roots 4 real roots 2 real roots 0 real roots in matlab

To find the number of real roots of a function in a specific interval in MATLAB, you can use the following steps:

1. Define the function f(x) = exp(-x^2) * sin(5*x) in MATLAB.

2. Use the fzero function to find the roots of the function within the interval [-1, 1].

3. Count the number of roots found in the interval. If there are 0 roots, the function has 0 real roots. If there is 1 root, the function has 1 real root. If there are 2 roots, the function has 2 real roots. If there are 3 roots, the function has 3 real roots. If there are 4 roots, the function has 4 real roots.

Here is a code snippet that demonstrates this:

main.m
% Define the function
f = @(x) exp(-x.^2) .* sin(5*x);

% Find the roots within the interval [-1, 1]
roots = fzero(f, [-1, 1]);

% Count the number of roots
num_roots = length(roots);

% Display the number of roots
disp(['Number of real roots: ', num2str(num_roots)]);
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You can run this code in MATLAB to determine the number of real roots of the function f(x) = exp(-x^2) * sin(5*x) in the interval [-1, 1].