Exercise 13 1. For each problem, find the average value of the function over the given interval. Give answer in exact value if applicable. (a) f(x) = 8x - 3+5e2-x, [0,2] [Ans: = (5 + 5e2) ] (b) f(x) = cos(2x) - sin (), [-7. ~] [Ans: - 2V2 3 TC 2. Find the average value of the function f (x) = 4x2 - x + 5 on [-2,3] and determine the value(s) of c in [-2,3] for which f (c) is equal to the average value of the function on 427 83 1+ 3 [-2,3]. Ans: C = 6 8Exercise 14 1 . An object starts from rest and has an acceleration of a (t) = t2. a) What is its velocity after 3 seconds? [Ans: 9] b) What is its position after 3 seconds? [Ans: - 2. A particle travels in a straight line so that, t seconds after passing a fixed point A on the line, its acceleration, a ms-2, is given by a =-2 - 2t. It comes to rest at a point B when t = 4. a) Find the velocity of the particle at A. b) Find the distance AB