Exam 3

On this exam you may use your calculator to check yourself, to find derivatives, and to solve equations. But you must show work. (1) Evaluate: $\sum_{i=1}^{8} (i-1)$

(2) Evaluate:

(a) $\int (2x^2+\frac{1}{x})\sqrt{x} dx$

(b) $\int \frac{x^2+x}{x^3} dx$

(3) Evaluate $\triangle y$ and dy for y=2x-2x³ where x=0 and dx =.01.

(4) Find a linear approximation to the curve $y=\tan x - x$ at the point $(\pi,-\pi)$.

(5) A rancher has a large bull that he wishes to sell. He is in the process of fattening the steer in order to get more for it. The bull now weighs 700 pounds, and it is expected that it will gain 50 pounds per week. But the market is dropping off. Currently the bull will go for 80 cents per pound, but there is an expected drop off of 2 cents per pound per week for the near future. When should he sell the bull to maximize revenue?

(6) Two vertical polls are separated by a distance of 20 feet. The first is 6 feet tall while the second is 8 feet tall. A rope will be attached to the top of one of the polls, run to a point on the ground between the two polls, and then attached to the top of the other poll. Where should the point on the ground be located to obtain the shortest length rope that can achieve this? (Minimize the length of the rope by adjusting the point on the ground)

(A calculator will very much help you with the algebra in this problem)