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# Test4 - d âˆ dx x 3 5(10 pts a Suppose the t C represents...

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Name: ____________________________ Calculus Test #4 (Chapter 5) SHOW ALL WORK!!! 1. (15 pts.) a) Use the limit definition to evaluate 3 2 2 dx x b) Use the Fundamental Theorem of Calculus to check your answer from part a.

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2. (20 pts.) The graph of ( ) f t is given below. Let 0 ( ) ( ) x F x f t dt = a) Find ) 2 ( F b) Find ) 6 ( F c) At what value(s) of x does ) ( x F attain its local minimum(s)? d) At what value of x does ) ( x F attain its global maximum? e) When is ) ( x F concave down? f) When is ) ( x F concave up?
3. (15 pts.) A car comes to a stop six seconds after the driver applies the brakes. While the brakes are on, the following velocities are recorded: a) Give an upper bound for the total distance traveled by the car. b) Give a lower bound for the total distance traveled by the car. t (sec) v ( t ) ft/sec 0 88 2 45 4 16 6 0

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4. (30 pts.) Find the following integrals: a. - - 2 1 0 2 1 1 ) ( sin dx x x b. + 1 0 2 1 3 dx x
c. dx x x xe x x

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Unformatted text preview: + d. âˆ« dx x 3 5. (10 pts.) a) Suppose the ) ( t C represents the daily cost of heating your house, measured in dollars per day, where t is time measured in days and = t corresponds to January 1, 2009. Interpret âˆ« 90 ) ( dt t C in words. b) If water is leaking out of a tank at a rate of ) ( t R gallons per hour, where t is measured in hours. Write a definite integral that expresses the total amount of water that leaks out in the first two hours. What units will the integral have? 6. (10 pts.) Estimate âˆ« 2 1 dx e x using right-hand endpoints with 3 subdivisions. Draw a picture of what you are doing and show all work. Extra Credit: Which of the following areas are equal? Why? (You must explain your answer, guessing will NOT give you any credit)...
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