Chapter62004solutions - Chapter 6 Test 1. Evaluate 1 1 dx...

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Chapter 6 Test December 7, 2004 Name 1. Evaluate 0 1 1 cccccccccccccccc cccccccccccccc x 2 + 2x + 1 dx = 0 1 1 cccccccccccccccc ccccccc H x + 1 L 2 dx u = x + 1, du = dx 1 2 u 2 du =− A 1 cccc u E 1 2 i k j j 1 cccc 2 1 y { z z = 1 cccc 2 2. Evaluate è!!! x i k j j è!!! x 3 + 4 y { z z dx = i k j j j j j x 5 cccc 6 + 4 x 1 cccc 2 y { z z z z z dx = 6 cccccc 11 x 11 cccccc 6 + 8 cccc 3 x 3 cccc 2 + C 3. Solve the initial value problem. Support your answer by overlaying your solution on a slope field for the differential equation. dy dx = 1 ccccccccccccccc x + 3 cccc 2 ,y i k j j 1 2 y { z z = 1 2 1 1 2 1 1 2 3 dy = · 1 ccccccccccccccc x + 3 cccc 2 dx y = ln ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ x + 3 cccc 2 ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ + C y = ln 1 + C = 1 C = 1 y = ln ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ x + 3 cccc 2 ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ + 1 4. Evaluate 1 y 2 sec i k j j j j 1 cccc y y { z z z z tan i k j j j j 1 cccc y y { z z z z dy u = 1 cccc y = y 1 ,du = 1 cccccc y 2 dy →− du = 1 y 2 dy sec u tan u du sec u + C sec i k j j j j 1 cccc y y { z z z z + C 5. Solve the following differential equation by the technique of separation of variables : dy dx = x è!!!
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This note was uploaded on 08/29/2010 for the course MATH 44323 taught by Professor Anderson during the Spring '09 term at University of California, Berkeley.

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Chapter62004solutions - Chapter 6 Test 1. Evaluate 1 1 dx...

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