(a) (b) Find the least squares approximation of f(x) = x2 + 3 over the interval [0, 1] by a function of the form y = ae? + bx, where a, b E R. You should write the coefficients a, b as decimal approximations, rounded to two decimal places. Let g(x) be the least squares approximation you found in the pre- vious problem. So g(x) = ae + bx for some scalars a, b. Find the least squares approximation of g(x) over the interval [0, 1] by a function of the form cx? +d. You should write the coefficients c, d as decimal approximations, rounded to two decimal places. Let h(x) be the function you found in part (b), and g(x) the function you found in part (a). Without actually doing any integral computations, decide which of the following facts must be true: i. Sof(g(x) (x2 + 3))?dx > Sof(g(x) h(x))dx ii. S (g(x) (x2 + 3))?da 5 S (g(x) h(x))?dx And justify your assertion. (c) (a) (b) Find the least squares approximation of f(x) = x2 + 3 over the interval [0, 1] by a function of the form y = ae? + bx, where a, b E R. You should write the coefficients a, b as decimal approximations, rounded to two decimal places. Let g(x) be the least squares approximation you found in the pre- vious problem. So g(x) = ae + bx for some scalars a, b. Find the least squares approximation of g(x) over the interval [0, 1] by a function of the form cx? +d. You should write the coefficients c, d as decimal approximations, rounded to two decimal places. Let h(x) be the function you found in part (b), and g(x) the function you found in part (a). Without actually doing any integral computations, decide which of the following facts must be true: i. Sof(g(x) (x2 + 3))?dx > Sof(g(x) h(x))dx ii. S (g(x) (x2 + 3))?da 5 S (g(x) h(x))?dx And justify your assertion. (c)