MAT 1322M1 Winter2005

MAT 1322M1 Winter2005 - MAT 1322, Winter 2005 SOLUTIONS TO...

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Unformatted text preview: MAT 1322, Winter 2005 SOLUTIONS TO TEST 1 (Version 1) 1. [2 points, 5.10 #17] Determine if the integral R ∞ xe − 3 x dx is convergent or divergent and evaluate if it is convergent. A. 0 . 25 B. 0 . 11 C. 0 . 125 D. 0 . 333 E. 0 . 0625 F. divergent Solution . By parts: u = x, v = e − 3 x , u = 1 , v = − 1 3 e − 3 x R ∞ xe − 3 x dx = − 1 3 xe − 3 x + 1 3 R e − 3 x dx ∞ = − 1 3 xe − 3 x − 1 9 e − 3 x ∞ = 0 + 1 9 . = 0 . 11 2. [2 points, 6.1 #9] Find the area of the region enclosed by the curves y = 3 x 2 and y = 4 − 3 x 2 . A. 5 . 33 B. 3 . 37 C. 9 . 01 D. 6 . 11 E. 2 . 92 F. 4 . 35 Intersection: 3 x 2 = 4 − 3 x 2 , 6 x 2 = 4 , x = ± p 2 / 3 A = R √ 2 / 3 − √ 2 / 3 (4 − 3 x 2 − 3 x 2 ) dx = R √ 2 / 3 − √ 2 / 3 (4 − 6 x 2 ) dx = 4 x − 2 x 3 √ 2 / 3 − √ 2 / 3 = 2 4( 2 3 ) 1 / 2 − 2( 2 3 ) 3 / 2 = 4 . 35 3. [2 points, 6.2 #13] The region enclosed by the curves y = 3 √ x, x = 1 , y = 0 is rotated about the line y = 2. Find the volume of the resulting solid. A. 12 . 25 B. 8 . 73 C. 7 . 54 D. 10 . 01 E. 6 . 66 F. 9 . 25 Solution . V = R 1 π (2 2 − (2 − x 1 3 ) 2 ) dx = = R 1 π (4 − 4 + 4 x 1 3 − x 2 3 ) dx = = π h 3 x 4 3 − 3 5 x 5 3 i 1 = 12 π 5 = 7 . 54 4. [2 points, 6.2 #25] A pyramid of height 8m has a square base of dimension 4m × 4m. Find its volume (in m 3 ). A. 36 . B . 2 5 . 25 C. 42 . 67 D. 40 . 72 E. 55 . 21 F.27 . Solution . A cross-section at height y is a square whose side s satisfies s/ (8 − y ) = 4 / 8 by similar triangle....
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This note was uploaded on 02/23/2010 for the course MAT MAT1332 taught by Professor Arianemasuda during the Fall '09 term at University of Ottawa.

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MAT 1322M1 Winter2005 - MAT 1322, Winter 2005 SOLUTIONS TO...

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