Test 3 - 31L Test#3(spring 2009 Tomberg Name I reaffirm the...

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31L Test #3 (spring, 2009, Tomberg) Name______________________________ I reaffirm the Duke Community Standard. You must clearly show all your work on each problem to receive full credit. work may Unsupported receive credit no . All integrals should be worked out by hand unless you are instructed otherwise . If you have read the previous three sentences place an X in the following box. œ 1. Let be a continuous function on the interval [a,b]and let , , , , be a partition of 0 B &+BB ±B &, 0 12 8 [a,b] . Complete the following: We define to be______________________________________, ( a b 0—B².B where = ____________________. ? B 2. Environmentalists, monitoring the flow of waste water from a chemical plant, recorded the data in the table below. time (days ) 02468 1 0 12 waste water (hundred of gallons / day ) 4.0 0 3.5 0 1.7 5 0.6 5 0.2 4 0.1 5 0.15 a) Give upper and lower estimates for the amount of waste water that flowed from the plant during the 12 day period. Your answers should contain units. b) How often would the environmentalists have had to record the flow rate of the waste water in order for the error of their estimate to less than 10 gallons? Your answers should contain units. 3. Solve the initial value problem cos(5 ) , 3. .C .> & C > C—!²& 4. Solve the initial value problem 2 .> #B & B C / ³ C—!²& #
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5. Below you see the graphs of and If the area under between and is approximately 0 B 0—B& ± 0 BB ww 3 3²" ab 23 (the shaded region), what corresponding quantity on the graph of is 23? Illustrate your answer on the graph
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Test 3 - 31L Test#3(spring 2009 Tomberg Name I reaffirm the...

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