Let f (x) = (1 + x2 + x4 + . . . + x8) and g(x) = (1 + x/1! + x2/2! + . . . + x8/8! ) . (a) Define h(x) = f (x) g(x), h(x) is a polynomial of degree 8. Find the coeffi- cients of x0, x1, x2 and x3. (b) Define h(x) = f (x) g(x), h(x) is a polynomial of degree 16. Find the coeffi- cients respect to the powers x0, x1, x2 and x3 for the polynomial h(x). (c) Define h(x) = f (x2), h(x) is a polynomial of degree 16. Find the coefficients respect to the powers x0, x1, x2 and x3 for the polynomial h(x). (d) Define h(x) = g(x2), h(x) is a polynomial of degree 16. Find the coefficients respect to the powers x0, x1, x2 and x3 for the polynomial h(x). (e) Define h(x) = g(x), h(x) is a polynomial of degree 7. Find the coefficients of x0, x1, x2 and x3 for the polynomial h(x). (f) Define h(x) = g(x)dx, h(x) is a polynomial of degree 9. Find the coefficients respect to the powers x0, x1, x2 and x3 for the polynomial h(x)