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Unformatted text preview: Miller, Kierste Homework 2 Due: Jan 30 2007, 3:00 am Inst: Gary Berg 1 This printout should have 19 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Rewrite the sum n 2+ 1 9 2 o + n 4+ 2 9 2 o + ... + n 12+ 6 9 2 o using sigma notation. 1. 6 X i = 1 n 2 i + i 9 2 o correct 2. 6 X i = 1 n i + 2 i 9 2 o 3. 9 X i = 1 n 2 i + i 9 2 o 4. 6 X i = 1 2 n i + i 9 2 o 5. 9 X i = 1 2 n i + i 9 2 o 6. 9 X i = 1 2 n i + 2 i 9 2 o Explanation: The terms are of the form n 2 i + i 9 2 o , with i = 1 , 2 , ... , 6. Consequently, in sigma notation the sum becomes 6 X i = 1 n 2 i + i 9 2 o . keywords: Stewart5e, summation notation, 002 (part 1 of 1) 10 points Estimate the area, A , under the graph of f ( x ) = 4 x on [1 , 5] by dividing [1 , 5] into four equal subintervals and using right endpoints. Correct answer: 5 . 133 . Explanation: With four equal subintervals and right end points as sample points, A n f (2) + f (3) + f (4) + f (5) o 1 since x i = x * i = i + 1. Consequently, A 5 . 133 . keywords: Stewart5e, area, rational function, Riemann sum, 003 (part 1 of 1) 10 points Cyclist Joe accelerates as he rides away from 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 Compute best possible upper and lower es timates for the distance he travels over this period by dividing [0 , 5] into 5 equal subinter vals and using endpoint sample points. Miller, Kierste Homework 2 Due: Jan 30 2007, 3:00 am Inst: Gary Berg 2 1. 47 ft < distance < 61 ft 2. 47 ft < distance < 59 ft 3. 47 ft < distance < 63 ft 4. 49 ft < distance < 61 ft 5. 49 ft < distance < 63 ft 6. 45 ft < distance < 61 ft correct 7. 45 ft < distance < 63 ft 8. 49 ft < distance < 59 ft 9. 45 ft < distance < 59 ft Explanation: The distance Joe travels during the 5 sec ond period is the area under the velocity graph and above [0 , 5]. Since Joes speed is increasing, the best possible lower estimate occurs taking left hand endpoints as sample points and the area of the rectangles shown in 1 2 3 4 5 4 8 12 16 20 On the other hand, the best upper estimate will occur taking right hand endpoints and the area of the rectangles shown in 1 2 3 4 5 4 8 12 16 20 Consequently, reading off values from the graphs to compute the height of the rect angles, we see that 45 ft < distance < 61 ft . keywords: 004 (part 1 of 1) 10 points Stewart Section 5.1, Example 3(a), page 321 Decide which of the following regions has area = lim n n X i = 1 4 n tan i 4 n without evaluating the limit....
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This note was uploaded on 05/08/2008 for the course M 408 L taught by Professor Cepparo during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Cepparo

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