HW_2_Answers - Miller, Kierste Homework 2 Due: Jan 30 2007,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Miller, Kierste Homework 2 Due: Jan 30 2007, 3:00 am Inst: Gary Berg 1 This print-out should have 19 questions. Multiple-choice 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....
View Full Document

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.

Page1 / 11

HW_2_Answers - Miller, Kierste Homework 2 Due: Jan 30 2007,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online