This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Kim, Jin Homework 2 Due: Sep 11 2007, 3:00 am Inst: Diane Radin 1 This printout should have 20 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 3 n 2 + 4 n 2 + 3 n 2 + 8 n 2 + ... + 3 n 2 + 4 n n 2 using sigma notation. 1. n X i = 1 4 n 2 + 3 i n 2 2. n X i = 1 3 n 2 + 4 i n 2 correct 3. n X i = 1 3 n 2 i + 4 i n 2 4. n X i = 1 4 i n 2 + 3 i n 2 5. n X i = 1 3 i n 2 + 4 i n 2 6. n X i = 1 4 n 2 i + 3 i n 2 Explanation: The terms are of the form 3 n 2 + 4 i n 2 , with i = 1 , 2 , ... , n . Consequently in sigma notation the sum becomes n X i = 1 3 n 2 + 4 i n 2 . keywords: Stewart5e, summation notation, Riemann sum form 002 (part 1 of 1) 10 points Estimate the area, A , under the graph of f ( x ) = 1 x on [1 , 5] by dividing [1 , 5] into four equal subintervals and using right endpoints. Correct answer: 1 . 283 . 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 1 . 283 . keywords: Stewart5e, area, rational function, Riemann sum, 003 (part 1 of 1) 10 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 54 Kim, Jin Homework 2 Due: Sep 11 2007, 3:00 am Inst: Diane Radin 2 2. area 51 3. area 55 correct 4. area 52 5. area 53 Explanation: With 10 equal subintervals and right end points as sample points, area n f (1) + f (2) + ... f (10) o 1 , since x i = i . Consequently, area 55 , reading off the values of f (1) , f (2) , ..., f (10) from the graph of f . keywords: Stewart5e, graph, estimate area, Riemannn sum 004 (part 1 of 1) 10 points Estimate the area under the graph of f ( x ) = 3 sin x between x = 0 and x = 3 using five approx imating rectangles of equal widths and right endpoints as sample points. 1. area 1 . 807 2. area 1 . 767 correct 3. area 1 . 847 4. area 1 . 787 5. area 1 . 827 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 ] = h ( i 1) b n , ib n i and right endpoints x i as sample points is A n f ( x 1 ) + f ( x 2 ) + ... + f ( x n ) o b n . For the given area, f ( x ) = 3 sin x, b = 3 , n = 5 , and x 1 = 1 15 , x 2 = 2 15 , x 3 = 1 5 , x 4 = 4 15 , x 5 = 1 3 ....
View
Full
Document
This note was uploaded on 04/12/2010 for the course PHY 58195 taught by Professor Turner during the Spring '09 term at University of Texas at Austin.
 Spring '09
 Turner

Click to edit the document details