12. (12 points) Use Richardson extrapolation to improve your approximation of f: "(0) Consider f. (x) = sin( x) 13. (12 points) Use 5 points (4 subintervals) on the interval [0, 1] and the Trapezoidal Rule to approximate [ f. ( x ) ax 14. (12 points) Bound the error using the trapezoidal rule. 15. (24 points) Find such that the quadrature formula G and x f ( x) dx = c, f (1) +J ( x) 2 has the highest degree of precision possible