q3-sect7-F-2011

q3-sect7-F-2011 - PRINT Your Name: Quiz 3 — September 2,...

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Unformatted text preview: PRINT Your Name: Quiz 3 — September 2, 2011 – Section 7 – 10:10 – 11:00 Remove everything from your desk except a pencil or pen. Circle your answer. Show your work. coherent. CHECK your answer. The quiz is worth 5 points. √ 5 + 4x − x2 dx. Find Your work should be correct and Answer: Complete the square 5 + 4x − x2 = 5 + 4 − (x2 − 4x + 4 ) = 9 − (x − 2)2 . We let x − 2 = 3 sin θ . It follows that dx = 3 cos θdθ and 9 − (x − 2)2 = 9 − 9 sin2 θ = 9 cos2 θ . The original problem is 9 (1 + cos 2θ )dθ 5 + 4x − x2 dx = 9 − (x − 2)2 dx = 9 cos2 θdθ = 2 9 9 = (θ + (1/2) sin 2θ ) + C = (θ + sin θ cos θ ) + C 2 2 = 9 2 arcsin x−2 3 = 9 2 arcsin x−2 3 = 9 arcsin 2 x−2 3 9 − (x − 2)2 +C 3 √ x − 2 5 + 4 x − x2 + +C 3 3 + x−2 3 1 + (x − 2) 5 + 4x − x2 + C 2 Check. The derivative of the proposed answer is 9 2 = 9 2 = 1/3 1− x−2 2 3 4 − 2x + (1/2) (x − 2) √ + 2 5 + 4 x − x2 1/3 1 3 2−x + + (1/2) (x − 2) √ 2 5 + 4 x − x2 9 − (x − 2) 5 + 4 x − x2 5 + 4 x − x2 2−x 9 1 √ + (1/2) (x − 2) √ + 5 + 4 x − x2 2 2 5 + 4x − x 5 + 4 x − x2 1 9 − (x − 2)2 + 5 + 4x − x2 =√ 2 5 + 4 x − x2 1 =√ 2(5 + 4x − x2 ) = 5 + 4x − x2 . 2 5 + 4 x − x2 1 ...
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This note was uploaded on 10/12/2011 for the course MATH 142 taught by Professor Kustin during the Fall '11 term at South Carolina.

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