find me a rational approximation of pade of the function sin(2x-3) throu a function (p_0+p_1x+p_2x^2+p_3x^3+p_4x^4+p_5x^5)/(1+q_1x+q_2x^2+q_3x^3+q_4x^4+q_5x^5) for m=n=5 on the interval [-2,2] in matlab

To find a rational approximation of the function sin(2x-3) using the Pade approximation in MATLAB, you can follow these steps:

Step 1: Define the function to be approximated

main.m
f = @(x) sin(2*x - 3);
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Step 2: Define the order of the Pade approximation (m and n)

main.m
m = 5; % numerator order
n = 5; % denominator order
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Step 3: Define the interval for approximation

main.m
x = linspace(-2, 2);
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Step 4: Generate the Pade approximation coefficients using the pade function

main.m
[p,q] = pade(f(x), m, n);
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Step 5: Construct the rational approximation function

main.m
p_approx = polyval(p, x) ./ (1 + polyval(q, x));
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Step 6: Plot the original function and the rational approximation

main.m
plot(x, f(x), 'b', x, p_approx, 'r');
legend('Original Function', 'Rational Approximation');
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This will approximate the given function using a rational approximation of Pade order 5/5 on the interval [-2, 2].

Note: The pade function is part of the Symbolic Math Toolbox in MATLAB and it calculates the Pade approximation coefficients.

Assuming you have the Symbolic Math Toolbox installed, this code should give you the desired rational approximation.