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8. (6 pts) Sand is being dumped from a conveyor belt at a ra…

8. (6 pts) Sand is being dumped from a conveyor belt at a rate of 35 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 feet high? Round your answer to four decimal places. Note that the volume of a cone is given by V = (1/3) πr2h where r is the radius of the base of the cone and h is the height of the cone.

13. (7 pts) A rectangular area adjacent to a river is to be…

13. (7 pts) A rectangular area adjacent to a river is to be fenced in, but no fencing is required on the side by the river. The total area to be enclosed is 102,900 square feet. Fencing for the side parallel to the river is $7 per linear foot, and fencing for the other two sides is $6 per linear foot. The four corner posts cost $15 apiece. Find the minimum cost of the fence and the dimensions that give this cost. Your answer must include: a drawing definitions of variables the domain of your cost function verification that you have found a minimum value instead of a maximum value

For questions 1 and 2, refer to the graph of y = f(x) shown…

For questions 1 and 2, refer to the graph of y = f(x) shown below.     1. (6 pts) For each value of a, find: the limit of f(x) as x approaches a from the left the limit of f(x) as x approaches a from the right the limit of f(x) as x approaches a f(a) a) a = -4 b) a = 2 c) a = 4     2. (4 pts) Use the same graph as in #1. Find the three x-values at which f(x) is discontinuous. For each one: a) Using concepts of limits, explain (briefly – a few words) why the function is discontinuous at this value. b) Classify the discontinuity as removable, jump, or infinite. You do not have to explain.