Please answer all questions and provide a brief explanation of the solution.

Question 1 7.7 pts Let f(z) and g(z) be two functions whose values at z = 0, 1, and 2 are given in the table below. 2 1(2) 8 9 ( 2 ) 0 1 -1 2 5 1 -1 2 7 3 If K(z) = f(g(z)), then K' (0) = O -5 O 15 35 Question 2 7.7 pts & S Vitrat Question 3 7.7 pts The position of a particle moving along the x-axis i sion z(t) = 13 - 3t? - 8t + 1, where t 2 0 is measured in seconds. Find all values of t for which the particle is at rest. Ot = 1 Ot= 1 and 1=3 Ot- 3 Question 4 7.7 pts Question 5 7.7 pts If So (4kx - 2x? )de = 36 , then k = Question 7.7 pts The area of the region enclosed by the graphs of y = z and y = z? - 32 + 3 is 01 02 Question 7 7.7 pts Let f be a continuous function that is defined for all real numbers z and that it has the following properties: off(z) dz = ( f f(z) dz = 10 Find the value of Sy (2/(z) + 6) dz . O 27 O 19. 0 17 Question 8 7.7 pts The volume of a cone is given by V = } with, where r is the radius of the circular base of the cone and h is the height of the cone. If the radius and the height are both increasing at the rate of 0.5 centimeters per second, then find IN in cubic centimeters per second when r = 6 cm and h = 9 cm . O 54 Question 9 7.7 pts The base of a solid is the region bounded by 4y = 23 and the line y = 2 with each cro dicular to the y-axis being a square. The volume of the solid is 0 8 O 32 Question 10 7.7 pts The region bounded by y = 13 , z = 2, and y = 0 is revolved about the line z - 2. The volume of the solid generated is O S 0 8 X Question 11 7.7 pts If z? + zy = 10. then when z = 2. 0- 2 - 2 Question 12 7.7 pts If f (z ) = = + 2 and g is the inverse of f, then s (10) = O-16 O 16 O =1 Question 13 7.6 pts The velocity of a particle moving on a line at time is . (t) - 5ti + 7ti meters per second. How many meters did the particle travel from -0 to $4? O 128 O 192 320 0 80