HW2 - momin (rrm497) Homework 02 cheng (58520) This...

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momin (rrm497) – Homework 02 – cheng – (58520) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – fnd 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 ) = 2 sin x between x = 0 and x = π 3 using fve approx- imating rectangles oF equal widths and right endpoints. 1. A 1 . 178 correct 2. A 1 . 138 3. A 1 . 098 4. A 1 . 118 5. A 1 . 158 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 ] = b ( i - 1) b n , ib n B and right endpoints x i as sample points is A ± f ( x 1 ) + f ( x 2 ) + . . . + f ( x n ) ² b n . ±or the given area, f ( x ) = 2 sin x, b = π 3 , n = 5 , and x 1 = 1 15 π, x 2 = 2 15 π, x 3 = 1 5 π, x 4 = 4 15 π, x 5 = 1 3 π . Thus A 2 ± sin( 1 15 π ) + . . . + sin( 1 3 π ) ² π 15 . AFter calculating these values we obtain the estimate A 1 . 178 For the area under the graph. 002 10.0 points Rewrite the sum ± 3+ p 1 9 P 2 ² + ± 6+ p 2 9 P 2 ² + . . . + ± 24+ p 8 9 P 2 ² using sigma notation. 1. 9 s i = 1 ± 3 i + p i 9 P 2 ² 2. 9 s i = 1 3 ± i + p 3 i 9 P 2 ² 3. 9 s i = 1 3 ± i + p i 9 P 2 ² 4. 8 s i = 1 ± i + p 3 i 9 P 2 ² 5. 8 s i = 1 3 ± i + p i 9 P 2 ² 6. 8 s i = 1 ± 3 i + p i 9 P 2 ² correct Explanation: The terms are oF the Form ± 3 i + p i 9 P 2 ² , with i = 1 , 2 , . . . , 8. Consequently, in sigma notation the sum becomes 8 s i = 1 ± 3 i + p i 9 P 2 ² . 003 10.0 points
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momin (rrm497) – Homework 02 – cheng – (58520) 2 Estimate the area, A , under the graph of f ( x ) = 5 x on [1 , 5] by dividing [1 , 5] into four equal subintervals and using right endpoints. 1. A 77 12 correct 2. A 25 4 3. A 37 6 4. A 19 3 5. A 73 12 Explanation: With four equal subintervals and right end- points as sample points, A b f (2) + f (3) + f (4) + f (5) B 1 since x i = x * i = i + 1. Consequently, A 5 2 + 5 3 + 5 4 + 1 = 77 12 . 004 10.0 points The graph of a function f on the interval [0 , 10] is shown in 2 4 6 8 10 2 4 6 8 Estimate the area under the graph of f by dividing [0 , 10] into 10 equal subintervals and using right endpoints as sample points. 1. area 48 2. area 51 3. area 50 4. area 52 correct 5. area 49 Explanation: With 10 equal subintervals and right end- points as sample points, area b f (1) + f (2) + . . . f (10) B 1 , since x i = i . Consequently, area 52 , reading oF the values of f (1) , f (2) , . . ., f (10) from the graph of f . 005 10.0 points Cyclist Joe brakes as he approaches a stop sign. His velocity graph over a 5 second period (in units of feet/sec) is shown in 1 2 3 4 5 4 8 12 16 20
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momin (rrm497) – Homework 02 – cheng – (58520) 3 Compute best possible upper and lower es- timates for the distance he travels over this period by dividing [0 ,
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HW2 - momin (rrm497) Homework 02 cheng (58520) This...

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