(Solution) - Obtain the least squares approximation polynomial of degree 3 for -(2025 Original AI-Free Solution)

Paper Details

Obtain the least squares approximation polynomial of degree 3 for the functions in Exercise 1 using the results of Exercise 7.
In Exercise 1
a. f (x) = x2 + 3x + 2, [0, 1];
b. f (x) = x3, [0, 2];
c. f (x) = 1/x, [1, 3];
d. f (x) = ex , [0, 2];
e. f (x) = 1/2 cos x + 1/3 sin 2x, [0, 1];
f. f (x) = x ln x, [1, 3].