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Unformatted text preview: Su, Yung – Homework 2 – Due: Sep 11 2007, 3:00 am – Inst: Shinko Harper 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 6 n ‡ 2 + 3 n · 2 + 6 n ‡ 2 + 6 n · 2 + ... + 6 n ‡ 2 + 3 n n · 2 using sigma notation. 1. n X i = 1 3 n ‡ 2 i + 6 i n · 2 2. n X i = 1 6 n ‡ 2 i + 3 i n · 2 3. n X i = 1 3 i n ‡ 2 + 6 i n · 2 4. n X i = 1 6 i n ‡ 2 + 3 i n · 2 5. n X i = 1 3 n ‡ 2 + 6 i n · 2 6. n X i = 1 6 n ‡ 2 + 3 i n · 2 correct Explanation: The terms are of the form 6 n ‡ 2 + 3 i n · 2 , with i = 1 , 2 , ... , n . Consequently in sigma notation the sum becomes n X i = 1 6 n ‡ 2 + 3 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 ) = 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 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 Su, Yung – Homework 2 – Due: Sep 11 2007, 3:00 am – Inst: Shinko Harper 2 2. area ≈ 55 3. area ≈ 56 4. area ≈ 52 correct 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 ≈ 52 , 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 ) = 4 sin x between x = 0 and x = π 4 using five approx imating rectangles of equal widths and right endpoints as sample points. 1. area ≈ 1 . 431 2. area ≈ 1 . 391 correct 3. area ≈ 1 . 371 4. area ≈ 1 . 411 5. area ≈ 1 . 451 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 ) = 4 sin x, b = π 4 , n = 5 , and x 1 = 1 20 π, x 2 = 1 10 π, x 3 = 3 20 π, x 4 = 1 5 π, x 5 = 1 4 π ....
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This note was uploaded on 04/15/2009 for the course M 59685 taught by Professor Harper during the Spring '09 term at University of Texas at Austin.
 Spring '09
 Harper
 Calculus

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