30_new - a b then the area between the graphs of f and g is...

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– DiscGQ01 – gilbert – (55035) 1 This print-out should have 3 questions. Multiple-choice questions may continue on 6 the next column or page find all choices before answering. 1. 4 correct 001 10.0 points 2 Find the derivative of f when f (x) = 5 sin 1 x 5 + p 25 − x 2 . −2 2 2 4 6 1 1. f (x) = 5 − x 2. f (x) = r 5 + x 5 − x 2. 6 3. f (x) = r 5 − x correct 4 5 + x 5 2 4. f (x) = 25 x 2 x 5. f (x) = 25 x 2 2 4 6 1 6. f (x) = 5 + x Explanation: 2 By the Chain Rule, 5 x 3. f (x) = 25 x 2 − √ 25 x 2 −2 −2 4 6 = 5 x . On the other hand, 25 x 2 4 25 − x 2 = (5 − x)(5 + x) . −6 Consequently, f (x) = r 5 − x . 5 + x 2 002 10.0 points 4. 2 4 6 For which one of the following shaded re- −2 gions is its area represented by the integral −4 0 4 (x + 1) + 2 1 x dx ? −6
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– DiscGQ01 – gilbert – (55035) 2 about the x -axis. 6 = 1 5. 1. V π 4 6 2 2. V = 2 π correct 3 3. V = 2 −2 2 4 6 3 −2 4. V = 1 6 Explanation: If f ( x ) ≥ g ( x ) for all x in an interval [
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Unformatted text preview: a, b ], then the area between the graphs of f and g is given by Area = A B f ( x ) − g ( x ) dx . ë o When f ( x ) = x + 1 , g ( x ) = − 1 2 x , therefore, the value of 4 ( x + 1) + 2 1 x dx ë o is the area of the shaded region 5. V = 1 3 π 6. V = 1 3 Explanation: The volume of the solid of revolution ob-tained by rotating the graph of y = f ( x ) on [ a, b ] about the x-axis is given by volume = π A B f ( x ) 2 dx . When f ( x ) = x 2 , a = 2 , b = 3 , 6 therefore, 4 . V = π 2 3 x 4 2 dx . 2 Consequently, −2 4 6 V = π Ž − x 4 ₃ 2 3 = 3 2 π . keywords: AreaBetween, AreaBetweenExam, 003 10.0 points Find the volume, V , of the solid obtained by rotating the region bounded by y = x 2 , x = 2 , x = 3 , y =...
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30_new - a b then the area between the graphs of f and g is...

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