test 4 in class

test 4 in class - R10 Answer these questions for a hint and...

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Name: _________________ Test #4 Integrals In-class portion No Calculators 1. 0 4 t 2 t 2 1 2 1 dt Find the average value of this function over the interval [0, 4] 2. Find the general solution to the equation dy dx = x 2 y Find the particular solution to the equation that passes through the point (2, 5 e 2 ). What is the slope of the graph at that point? 3. Consult the following table of integrals for two continuous functions f and g over [ a , b ]: Interval [ a , b ] [ b , c ] [ c , d ] [ d , e ] Definite integral of f ( x ) a b f x dx = 10 b c f x dx = 12 c d f x dx = 10 d e f x dx = 4 Definite integral of g ( x ) a b g x dx = 8 a b f x dx = 15 a b f x dx = 18 a b f x dx = 9 A. a d f x dx = B. c b g x dx = C. a a g x dx = D. Let h ( x ) be defined as f ( x ) – g ( x ). a d h x dx = E. Can we determine at what points f ( x ) = g ( x )? If so, when? If not, why not? 4. x x 9 dx =
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5. Consider the following graph What is the maximum error in estimating the area under the curve over the interval [-6, 4] for L10 or
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Unformatted text preview: R10? Answer these questions for a hint, and partial credit: What is the formula for finding the maximum error? What do you get if you apply that formula to this curve? What is the problem with that? How might you fix the problem? So, what is the maximum error? EC: The function f ( t ) is defined as the area under the curve to the right between 0 and t : f t = ∫ t x 2 − 1 dx What is f (1)? f (5)? f (-2)? At what point(s) is f ( x ) = 0? What is the instantaneous rate of change at t = 2? (How much is f changing by at that exact point?) What is f '( t )? 5 4 3 2 1-1-6-4-2 2 4 6 . . . . 5 4 3 2 1-1 2 4 6 . ....
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This note was uploaded on 02/28/2012 for the course MATH 160 taught by Professor Staff during the Spring '08 term at Boise State.

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test 4 in class - R10 Answer these questions for a hint and...

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