Question

2) An object is thrown upward with an initial velocity of 144 feet per second from an initial height of 160 feet. Use the fact that the acceleration due to gravity is -32 feet per second per second to answer the following: a) Using integration, find the position function giving the height s as a function of time t. b) At what time will the ball reach maximum height? c) When does the ball hit the ground? d) What is the maximum height of the ball? e) At what velocity does the ball hit the ground?


3) Use 5 rectangles to approximate the area under the region lying between the graph of ?(?) = ?3, the x-axis, x = 0 and x = 3 using upper sums (circumscribed rectangles). Construct a picture of the area you are finding.   


4) Find the derivative of the following functions. Explain the method you used to find the derivative: a) ?(?) = 4?9 − 7?5 − 3 ?4 + 5? − 8

b) ⁡ℎ(?) =
7?4 ????


c) ℎ(?) = 6?2cos(2?3)


5) Find the equation of the tangent line to the graph of the function ℎ(?) = 4?3 4?3−2 at ? = 1


6) A rancher wants to construct an area where he can keep his horses. He has 1450 feet of fencing with which to enclose two adjacent rectangular spaces which are separated by a fence. The rectangular spaces are of equal sizes. What dimensions should be used so that the enclosed area will be a maximum? (Hint: draw a sketch of the area, making sure to account for the problem having 2 equally sized rectangles.)

Answer 1