(7) Compute the 4th degree Taylor polynomial Ta(x) of f(x) = 4 + 3 + x2 + x + 1 at a = 0 (i.e., centered at (). Show your work. (8) Compute the exact error RA (x) = f(x) -T. (x). (9) Given an infinitely differentiable function f with f" (x) = - 1 Vati . If T3 (I) = Zio dark can be used to approximate f near = = 0, what should be the value of the coefficient a,? Explain your answer and show your work. (10) Compute the 5th degree Maclaurin polynomial M(x) (i.e. the 5th degree Taylor polynomial centered at 0) for f(x) = sin(x). Show your work. (a) Use Taylor's Remainder Theorem to express the remainder in using M(x) to approimate f at the point * = 15 [That is, express As 12 for some point ce (0, #).] (b) Find a bound for the magnitude of the remainder when using Ms 12 to approximate sin 12 (c) Graph the functions f and M on the same Cartesian plane. Also, plot the points 5, sin 12 and : M$ 17 Compute (use your calculator )sin 12 - M5 12 and interpret this on your graph. How does your calculation compare to your answer in part (b)? Explain