expand f (x, y)= e^xln(1+y) in terms of x and y upto the terms of 3rd degree using taylor series. in matlab

To expand the function f(x, y) = e^xln(1+y) in terms of x and y up to the terms of 3rd degree using Taylor series in MATLAB, you can follow these steps:

1. Define the function f(x, y) as a symbolic expression in MATLAB.

main.m
syms x y;
f(x, y) = exp(x)*log(1+y);
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2. Use the taylor function in MATLAB to approximate the function f(x, y) up to the 3rd degree terms. The taylor function takes two arguments: the function to be approximated and the degree of the approximation.

main.m
approximation = taylor(f, [x, y], 'Order', 3);
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3. Display the result of the approximation.

main.m
approximation
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This will give you the expanded form of the function f(x, y) up to the 3rd degree terms in terms of x and y using Taylor series in MATLAB.