Project #69920 - Calculus Problem set

1.)  Let f be an even function, let g be an odd function, and let h(x)=f(x)+g(x) for all x. If  ,  , and  , find the value of each of the following, if possible.

 

a.)   

b.)  

c.)   

d.)  

e.)    The average value of f(x) for

 

 

 

2.)  A tank which initially contains 225 gallons of water is drained according to the drainage rate information given in the table below.

Time(h)

0

1

2

3

4

5

6

Drainage Rate (gal/h)

40.9

33.5

27.4

22.5

18.4

15.1

12.3

 

a.)   Use a trapezoidal approximation to estimate the amount of water that has been drained during the first six hours.

b.)  Assuming that after six hours the water continues to drain at the rate of 12.3 gallons per hour, use your estimate from part (a) to find the total amount of time it takes to drain the tank completely.

c.)   Sketch a graph of the given drainage rate data.

d.)  Assume that the drainage rate is given by a smooth function r, where the graph of y=r(t) passes through the points you drew in part (c). Tell whether each of your answers to parts (a) and (b) are underestimates or overestimates. Explain.

Subject Mathematics
Due By (Pacific Time) 05/07/2015 12:00 am
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