The Maclaurin series can be used to represent certain functions such as the one

Question

The Maclaurin series can be used to represent certain functions such as the one below. cos x = sigma_k=0^infinity (-1)^k x^2k/(2k)! = 1 - x^2/2! + x^4/4! - x^6/6! + ... For this problem write a script that will compare the accuracy of the Maclaurin series to a definite integral. To do this: Create a symbolic expression for: x cos x Integrate the symbolic expression: integral_0^0.95 x cos x dx Use a for loop to construct the first 15 terms of the Maclaurin series: sigma_n=0^15 (-1)^k x^2 k/(2k)! Integrate the Maclaurin series: integral_0^0.95 x (1 - x^2/2! + x^4/4! - x^6/6! + ...) dx Find the absolute value of the difference between the two results. Now instead of doing the 15 terms, use a while loop and figure out how many terms you need to get error

Explanation / Answer

syms x

%1
f1 = (x*cos(x));

%2 Definite Integrals

f1
I1 = integral(f1,0,0.95);

%3 Maclaurin series

for n=0:15
trems(n+1) = ((-1).^n + x.^(2*k))/factorial(2*n);
end

%4
I2 = integral(trems,0,0.95);

%5 absolute vlaue
result = abs(I1 - I2);

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