MATH 114, WORKSHEET #8 FALL 2016 1. (10 points) On the same side of a straight river are two towns, and the townspeople want to build a pumping station P. The pumping station is to be at the river's edge with pipes extending straight to the two towns. The town 1 is 1 km from the river's edge and town 2 is 4 km from the river's edge. If A denotes the point on the river's edge closest to town 1 and B denotes the point at the river's edge closest to town 2, the distance from A to B is 4 km. Where should be the pumping station located to minimize the total length of pipe? 2. (8 + 2 =10 points) An object is thrown vertically upward with a speed of 10 m/sec from a height of 2 meters. (a) Find the highest point it reaches (b) When the object will hit the ground? HINT: An object moving under the influence of gravity has constant acceleration g = 9.8 m/sec2 ; thus, measuring distance from the ground dv = 9.8 m/sec2 . dt 3. (4 +6 = 10 points) (a) The graph of a certain function f has the slope 4x3 5 at each point (x, y) and the line x + y = 0 is the tangent line to the graph. Find the function f . (b) Evaluate the limit: lim n n \u0012 X (i 1)3 1 n4 \u0013 20 . n