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# solution2_pdf - Horstman(mdh995 – Homework02 – Radin...

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Unformatted text preview: Horstman (mdh995) – Homework02 – Radin – (58505) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Stewart Section 5.1, Example 3(b), page 321 Estimate the area, A ,under the graph of f ( x ) = 3 sin x between x = 0 and x = π 4 using five approx- imating rectangles of equal widths and right endpoints. 1. A ≈ . 963 2. A ≈ 1 . 003 3. A ≈ 1 . 023 4. A ≈ . 983 5. A ≈ 1 . 043 correct Explanation: An estimate for the area, A , under the graph of f on [0 , b ] with [0 , b ] partitioned in n equal subintervals [ x i- 1 , x i ] = bracketleftBig ( i- 1) b n , ib n bracketrightBig and right endpoints x i as sample points is A ≈ braceleftBig f ( x 1 ) + f ( x 2 ) + . . . + f ( x n ) bracerightBig b n . For the given area, f ( x ) = 3 sin x, b = π 4 , n = 5 , and x 1 = 1 20 π, x 2 = 1 10 π, x 3 = 3 20 π, x 4 = 1 5 π, x 5 = 1 4 π . Thus A ≈ 3 braceleftBig sin( 1 20 π ) + . . . + sin( 1 4 π ) bracerightBig π 20 . After calculating these values we obtain the estimate A ≈ 1 . 043 for the area under the graph. 002 10.0 points Rewrite the sum braceleftBig 5+ parenleftBig 1 9 parenrightBig 2 bracerightBig + braceleftBig 10+ parenleftBig 2 9 parenrightBig 2 bracerightBig + . . . + braceleftBig 30+ parenleftBig 6 9 parenrightBig 2 bracerightBig using sigma notation. 1. 9 summationdisplay i = 1 5 braceleftBig i + parenleftBig 5 i 9 parenrightBig 2 bracerightBig 2. 6 summationdisplay i = 1 braceleftBig 5 i + parenleftBig i 9 parenrightBig 2 bracerightBig correct 3. 6 summationdisplay i = 1 braceleftBig i + parenleftBig 5 i 9 parenrightBig 2 bracerightBig 4. 6 summationdisplay i = 1 5 braceleftBig i + parenleftBig i 9 parenrightBig 2 bracerightBig 5. 9 summationdisplay i = 1 braceleftBig 5 i + parenleftBig i 9 parenrightBig 2 bracerightBig 6. 9 summationdisplay i = 1 5 braceleftBig i + parenleftBig i 9 parenrightBig 2 bracerightBig Explanation: The terms are of the form braceleftBig 5 i + parenleftBig i 9 parenrightBig 2 bracerightBig , with i = 1 , 2 , . . . , 6. Consequently, in sigma notation the sum becomes 6 summationdisplay i = 1 braceleftBig 5 i + parenleftBig i 9 parenrightBig 2 bracerightBig . 003 10.0 points Horstman (mdh995) – Homework02 – Radin – (58505) 2 Estimate the area, A , under the graph of f ( x ) = 3 x on [1 , 5] by dividing [1 , 5] into four equal subintervals and using right endpoints. 1. A ≈ 15 4 2. A ≈ 73 20 3. A ≈ 77 20 correct 4. A ≈ 37 10 5. A ≈ 19 5 Explanation: With four equal subintervals and right end- points as sample points, A ≈ braceleftBig f (2) + f (3) + f (4) + f (5) bracerightBig 1 since x i = x * i = i + 1. Consequently, A ≈ 3 2 + 1 + 3 4 + 3 5 = 77 20 ....
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solution2_pdf - Horstman(mdh995 – Homework02 – Radin...

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