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Pre-Calc Homework Solutions 283

# Pre-Calc Homework Solutions 283 - Chapter 6 Review d(y dx 1...

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25. } d ( d y x 9 ) } 5 2 x 2 } x 1 2 } d ( y 9 ) 5 1 2 x 2 } x 1 2 } 2 dx E d ( y 9 ) 5 E 1 2 x 2 } x 1 2 } 2 dx y 9 5 x 2 1 x 2 1 1 C y 9 (1) 5 2 1 C 5 1 C 5 2 1 y 9 5 x 2 1 x 2 1 2 1 E dy 5 E ( x 2 1 x 2 1 2 1) dx y 5 } 1 3 } x 3 1 ln x 2 x 1 C y (1) 5 } 1 3 } 1 0 2 1 1 C 5 0 2 } 2 3 } 1 C 5 0 C 5 } 2 3 } y 5 } x 3 3 } 1 ln x 2 x 1 } 2 3 } Graphical support: Let f ( x ) 5 } x 3 3 } 1 ln x 2 x 1 } 2 3 } . We first show the graph of y 5 f 9 ( x ) 5 x 2 1 x 2 1 2 1, x . 0, along with the slope field for y 9 5 f 0 ( x ) 5 2 x 2 } x 1 2 } . [ 2 0.5, 4.21] by [ 2 9, 21] We now show the graph of y 5 f ( x ) along with the slope field for y 9 5 f 9 ( x ) 5 x 2 1 x 2 1 2 1. [ 2 0.5, 4.21] by [ 2 9, 21] 26. } d ( d r t 0 ) } 5 2 cos t d ( r 0 ) 5 2 cos t dt E d ( r 0 ) 5 E 2 cos t dt r 0 5 2 sin t 1 C r 0 (0) 5 C 5 2 1 r 0 5 2 sin t 2 1 E d ( r 9 ) 5 E ( 2 sin t 2 1) dt r 9 5 cos t 2 t 1 C r 9 (0) 5 1 1 C 5 2 1 C 5 2 2 r 9 5 cos t 2 t 2 2 E dr 5 E (cos t 2 t 2 2) dt r 5 sin t 2 } t 2 2 } 2 2 t 1 C r (0) 5 C 5 2 1 r 5 sin t 2 } t 2 2 } 2 2 t 2 1 Graphical support: We first show the graph of y 5 r 0 5 2 sin t 2 1 along with the slope field for
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