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Unformatted text preview: Chapter 6 Review
d(y ) dx 1 x2 1 2x dx x2 1 2x dx x2 d(r ) dt 283 25. 2x 26. cos t cos t dt cos t dt sin t C sin t ( sin t cos t 1 2 cos t (cos t sin t C sin t
t2 2 d(y ) d(y ) y y (1) C y dy y y (1)
2 3 d(r ) d(r ) r r (0) r x2 2 1 x C 1 C 1 C 1 1 1) dt C 1 d(r ) x2 (x 2 x
1 1 1 1) dx x C C 0 r r (0) C r dr r t x C 1 3 x ln x 3 1 0 1 3 t t 2 2) dt 2t C C C y 0
2 3 x3 3 ln x x 2 3 r(0) r 1
t2 2 Graphical support: Let f (x)
x3 3 2t 1 ln x x 2 . 3 Graphical support: We first show the graph of y f (x) x2 x f (x)
1 r r sin t cos t. 1 along We first show the graph of y x 1, 2x
1 . x2 with the slope field for y 0, along with the slope field for y [ 6, 4] by [ 3, 3] [ 0.5, 4.21] by [ 9, 21] Next, we show the graph of y f (x) along with the slope field
1 r cos t sin t 1. t 2 along We now show the graph of y for y f (x) x
2 with the slope field for y r x 1. [ 6, 4] by [ 3, 3] [ 0.5, 4.21] by [ 9, 21] Finally we show the graph of y along with the slope field for y r r sin t cos t t2 2 2t t 2. 1 [ 6, 4] by [ 8, 2] ...
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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.
 Spring '08
 GERMAN

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