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Unformatted text preview: Cheung, Anthony Homework 2 Due: Sep 12 2006, 3:00 am Inst: David Benzvi 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 n 5+ 1 9 2 o + n 10+ 2 9 2 o + ... + n 35+ 7 9 2 o using sigma notation. 1. 9 X i = 1 5 n i + i 9 2 o 2. 9 X i = 1 n 5 i + i 9 2 o 3. 7 X i = 1 n 5 i + i 9 2 o correct 4. 9 X i = 1 5 n i + 5 i 9 2 o 5. 7 X i = 1 n i + 5 i 9 2 o 6. 7 X i = 1 5 n i + i 9 2 o Explanation: The terms are of the form n 5 i + i 9 2 o , with i = 1 , 2 , ... , 7. Consequently, in sigma notation the sum becomes 7 X i = 1 n 5 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 ) = 5 x on [1 , 5] by dividing [1 , 5] into four equal subintervals and using right endpoints. Correct answer: 6 . 417 . 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 6 . 417 . keywords: Stewart5e, area, rational function, Riemann sum, 003 (part 1 of 1) 10 points Decide which of the following regions has area = lim n n X i = 1 4 n cos i 4 n without evaluating the limit. 1. n ( x, y ) : 0 y cos 2 x, x 8 o 2. n ( x, y ) : 0 y cos 3 x, x 4 o 3. n ( x, y ) : 0 y cos x, x 8 o 4. n ( x, y ) : 0 y cos 2 x, x 4 o 5. n ( x, y ) : 0 y cos x, x 4 o correct 6. n ( x, y ) : 0 y cos 3 x, x 8 o Explanation: Cheung, Anthony Homework 2 Due: Sep 12 2006, 3:00 am Inst: David Benzvi 2 The area under the graph of y = f ( x ) on an interval [ a, b ] is given by the limit lim n n X i = 1 f ( x i ) x when [ a, b ] is partitioned into n equal subin tervals [ a, x 1 ] , [ x 1 , x 2 ] , ..., [ x n 1 , x n ] each of length x = ( b a ) /n . When the area is given by A = lim n n X i = 1 4 n cos i 4 n , therefore, we see that f ( x i ) = cos i 4 n , x = 4 n , where in this case x i = i 4 n , f ( x ) = cos x, [ a, b ] = h , 4 i . Consequently, the area is that of the region under the graph of y = cos x on the interval [0 , / 4]. In setbuilder notation this is the region n ( x, y ) : 0 y cos x, x 4 o . keywords: limit Riemann sum, area, trig func tion 004 (part 1 of 1) 10 points Find an expression for the area of the region under the graph of f ( x ) = x 3 on the interval [5 , 9]....
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This note was uploaded on 01/27/2010 for the course M 408L taught by Professor Radin during the Spring '08 term at University of Texas at Austin.
 Spring '08
 RAdin
 Calculus

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