Chapter62005solutions

Chapter62005solutions - Chapter 6 Test 1. Evaluate H3x +...

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Chapter 6 Test December 6, 2005 Name 1. Evaluate H 3 x + 1 L 2 cccccccccccccccc ccccccccc 3 x dx = 3 2x + 23 x + 1 cccccccccccccccccccccccccccccccc ccccccccccc 3 x dx = H 3 x + 2 + 3 x L dx = 1 cccccccccc ln 3 3 x + 1 cccccccccc ln 3 3 x + C 2. Evaluate 3 π cccccccc 2 9 π ccccccc 4 cot i k j j x cccc 3 y { z z dx u = x cccc 3 so du = 1 cccc 3 dx or 3 du = dx 3 π cccc 2 3 π ccccccc 4 cot u du = 3 A ln sin u D π cccc 2 3 π ccccccc 4 = 3 i k j j j j j j ln i k j j j j j j è!!! 2 ccccccccc 2 y { z z z z z z ln 1 y { z z z z z z = 3ln i k j j j j j 1 ccccccccc è!!! 2 y { z z z z z = 3 I ln 1 ln è!!! 2 M = 3 ccccccc 2 ln 2 3. Solve the intial value problem. Support your answer by overlaying your solution on a slope field for the differential equation. dy dx = y cccc 2 ,y H 1 L = 1 cccc 2 2 1 1 2 1 1 2 3 dy dx = y cccc 2 1 cccc y dy = 1 cccc 2 dx 1 cccc y dy = 1 cccc 2 dx ln » y » = 1 cccc 2 x + C » y » = e x cccc 2 + C so y = Ae x cccc 2 and 1 cccc 2 = 1 2 A = è!!! e cccccccccc 2 so y = è!!! e ccccccccc 2 e x cccc 2 4. Evaluate 6 x e x dx = H 6 e L x dx = 1 cccccccccccccccc ccccc ln H 6e L H L x + C
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5. Solve the following differential equation H and isolate y L
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Chapter62005solutions - Chapter 6 Test 1. Evaluate H3x +...

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