Math 182

Quiz 3††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† Name:†† †††††††††††††† Key†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††

Show all work, and be sure to include units in your answers where appropriate

1.       What is the average value of the function



2.       A cable, with a mass of 2 kg / meter, is used to lift 20 kg of water from a well 6 meters deep.

How much work is done?


At a depth of x meters, the combined mass of the cable and the water is (2x+20)kg, which has a weight of

To lift this a small amount, say dx meters, requires (2x+20)(9.8)dx Joules

The total work is therefore

†††† $




††††††††††††††††††††††††††††††† Number sold (demand)


3.       For the demand function shown, what is the consumerís surplus if 600 units are sold at $20 each?


The consumerís surplus is the area of the region above the horizontal dashed line, and below the demand curve.This is a triangle with area (1/2)(600