# HW2 - momin(rrm497 Homework 02 cheng(58520 This print-out...

This preview shows pages 1–4. Sign up to view the full content.

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

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

View Full Document
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
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 ,

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

HW2 - momin(rrm497 Homework 02 cheng(58520 This print-out...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online