HW09-solutions

HW09-solutions - husain(aih243 – HW09 – Gilbert...

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Unformatted text preview: husain (aih243) – HW09 – Gilbert – (56215) 1 This print-out should have 31 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Rewrite the sum braceleftBig 2+ parenleftBig 1 9 parenrightBig 2 bracerightBig + braceleftBig 4+ parenleftBig 2 9 parenrightBig 2 bracerightBig + . . . + braceleftBig 14+ parenleftBig 7 9 parenrightBig 2 bracerightBig using sigma notation. 1. 9 summationdisplay i = 1 2 braceleftBig i + parenleftBig i 9 parenrightBig 2 bracerightBig 2. 9 summationdisplay i = 1 2 braceleftBig i + parenleftBig 2 i 9 parenrightBig 2 bracerightBig 3. 7 summationdisplay i = 1 braceleftBig 2 i + parenleftBig i 9 parenrightBig 2 bracerightBig correct 4. 7 summationdisplay i = 1 braceleftBig i + parenleftBig 2 i 9 parenrightBig 2 bracerightBig 5. 7 summationdisplay i = 1 2 braceleftBig i + parenleftBig i 9 parenrightBig 2 bracerightBig 6. 9 summationdisplay i = 1 braceleftBig 2 i + parenleftBig i 9 parenrightBig 2 bracerightBig Explanation: The terms are of the form braceleftBig 2 i + parenleftBig i 9 parenrightBig 2 bracerightBig , with i = 1 , 2 , . . . , 7. Consequently, in sigma notation the sum becomes 7 summationdisplay i =1 braceleftBig 2 i + parenleftBig i 9 parenrightBig 2 bracerightBig . 002 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 ≈ 50 2. area ≈ 52 3. area ≈ 51 correct 4. area ≈ 49 5. area ≈ 53 Explanation: With 10 equal subintervals and right end- points as sample points, area ≈ braceleftBig f (1) + f (2) + . . . f (10) bracerightBig 1 , since x i = i . Consequently, area ≈ 51 , reading off the values of f (1) , f (2) , . . ., f (10) from the graph of f . 003 (part 1 of 3) 10.0 points Below is the graph of a function f . husain (aih243) – HW09 – Gilbert – (56215) 2 1 2 3 − 1 − 2 − 3 2 4 6 8 − 2 − 4 − 6 (i) Estimate the definite integral I = integraldisplay 3 − 3 f ( x ) dx with six equal subintervals using right end- points. 1. I ≈ 10 correct 2. I ≈ 8 3. I ≈ 6 4. I ≈ 9 5. I ≈ 7 Explanation: Since [ − 3 , 3] is subdivided into six equal subintervals, each of these will have length 1 and the six corresponding rectangles are shown as the shaded areas in 1 2 3 − 1 − 2 − 3 2 4 6 8 − 2 − 4 − 6 The heights of the rectangles are right end- point sample values of f that can be read off from the graph. Thus, with right endpoints, I ≈ 1 − 4 − 1 + 3 + 4 + 7 = 10 . 004 (part 2 of 3) 10.0 points (ii) Estimate the definite integral I = integraldisplay 3 − 3 f ( x ) dx with six equal subintervals using left end- points....
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HW09-solutions - husain(aih243 – HW09 – Gilbert...

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