Pre-Calc Homework Solutions 298

Pre-Calc Homework Solutions 298 - 298 32. Section 7.2 (b)...

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Unformatted text preview: 298 32. Section 7.2 (b) The two areas in Quadrant I, where x c 4 y, are equal: y dy 0 c y dy 4 [ 0.5, 2.5] by [ 0.5, 1.5] y 1 x and y 2 1 intersect at x x2 1 dx x2 1 2 x 2 1 2 1 0 2 3/2 c 2 3/2 y y 3 3 0 c 2 3/2 2 3/2 2 3/2 c 4 c 3 3 3 1. Integrate in two parts: 1 x 2 1 2c 3/2 c 3/2 4 42/3 8 x dx 0 1 1 2 ( 1) 1 c . 24/3 c)-by- c 33. The curves intersect when sin x /4 cos x, i.e., at x /4 4 (c) Divide the upper right section into a (4 rectangle and a leftover portion: (cos x 0 sin x) dx sin x 2 1 cos x 0 0.414 0 c 2 (c 34. cx c [ 3, 3] by [ 2, 4] 3/2 x 2) dx 1 3 x 3 c (4 4 c) c c c (4 4x x 2) dx 1 3 x 3 2 c c3/2 c 3/2 0 1 3/2 c 3 4 c 8 (a) The curves intersect at x Use the region's symmetry: 2 2. 2 3/2 c 3 8 3 16 3 4 c 4 c 1 3/2 c 3 1 3/2 c 3 4 16 3 c c3/2 2 0 (3 x2 2 1) dx 2 0 (4 x 2) dx 1 3 x 3 8 3 2 0 4 3/2 c 3 2 4x 2 8 (b) Solve y 3 x 2 for x: x 1 and 3. 2 2 0 35. (a) 5 y=4 (2, 4) y=c (c, c) (c, c) y c3/2 0 32 3 4 42/3 24/3 c 36. 3 y. The y-intercepts are 3 2 1 3 y dy 2 (3 3 3 y)3/2 1 [ 1, 5] by [ 1, 3] 16 3 32 3 The key intersection points are at x Integrate in two parts: 1 0, x 1 and x 4. y = x2 (2, 4) 1 0 x 2 3/2 x 3 2 3 1 8 x dx 4 x2 8 1 4 1 2 x x dx 4 x2 8 4 1 x 3 x 4 0 x 4 1 (8 2) 1 8 11 3 If y ( x2 c, then x c. So the points are c, c) and ( c, c). ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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