Calculator Section For 0

Calculator Section For O < t < , aparticle moves along the y -axis. The velocity oftheparticle at time t is given by cot (20 + 7. The position of the particle is y 4 at time t 1 . 46. (a) Find the equation of a(t) , the acceleration ofthe particle for time O < t . 47. (b) At time t = 1 , is the panicle speeding up or slowing down? 48. (c) Find the position Of the particle at time t = . 49 (d) Another particle moves along the curve y +2xy = 7 . Find = 3 x2 and g (x) e2x 1 are shown in the figure. Let R be the shaded region The curves f (x) bounded by the graph off (x) , g(x) and the y -axis. 50. (a) Find the area of R using dy as your differential. 51. (b) Find the volume of the solid generated when R is rotated about the x -axis. 52. (c) The vertical line x = k divides R into two regions where the area of the region to the left ofthe line x = k is S the area of the region to the right of the line. Write, but do not solve, an equation involving integral expressions whose solution gives the value of k .