Test4Solutions - itG b Give a lower bound for the total...

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Name: ' A Calculus Test #4 (Chapter 5) 1 SHOW ALL WORK!!! 1 I .(IS po.)a) Use the limit definition to evaluate R .rn I i I - b) Use the Fundamental Theorem of Calculus to check your answer hm part a
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\ 2. (20 PW.) The graph of f (t) is given below. Let F(x) = 1 f (t)dt a) Find F(2) - I --2 4 F(2) = 5 2 ' (-2-2) - b) Find F(6) / c) At what vdue(s) of x does F(x) attain its local minimum(s)? at 8 = Y, f i x ) rnb ;ls lo& ~inimunt J d) At what value of x does F(x) attain its global maximum? e) When is F(x) concave down? f i x ) c a n c a ~ e d m m d ( o r 2 ? ~ ( ' 5 P 6 ) J f) When is F(x) concave up? tilo concaue up bf 1 2 15)-
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- ---- \ 3. (1s pb.1 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. v(k1 5 (08 '%$)(a*) itG - b) Give a lower bound for the total distance traveled by the car.
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Unformatted text preview: itG - b) Give a lower bound for the total distance traveled by the car. 1 4. (30 p ~ . , Find the following integrals: -I J sin % TC. I :. Jz u e d u . 0 1 i t 1 + C rmrx,=i;iu = t u 2 t C - u, Fcr)= (sin'x)ztc'- L ~ ( 3 -rcol J, c 5ii'l 2 ]'+C - + C~IR'OI -C 1 -11. = .[ sin - sin-' 0 1 5. (10 pa.) a) Suppose the C(t) represents the daily cost of heating your house, measured in dollars per day, where t is time measured in days and t = 0 corresponds to January 1,2009. Interpret C(t)dt in words. b) If water is leaking out of a iank at a rate of R(t) gallons per hour, where t is measured in hours. Write a definite integral that exprbses the total amount of water that leaks ,out in the fvst two hours. What units will the integral have? \ 6. (10 po.1 Estimate f ddr using right-hand endpoints with 3 subdivisions. h a w a picture of what you arc doing. and show all work....
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