Pre-Calc Homework Solutions 241

Pre-Calc Homework Solutions 241 - Section 6.2 66. Use...

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66. Use differential equation graphing mode. For reference, the equations of the solution curves are as follows. (0, 1): y 52} x 2 1 1 } (0, 2): y 52} 2 x 2 2 1 } (0, 2 1): y 52} x 1 1 1 } (0, 0): y 5 0 [ 2 2.35, 2.35] by [ 2 1.55, 1.55] The concavity of each solution curve indicates the sign of y 0 . 67. (a) } d d x } (ln x 1 C ) 5 } 1 x } for x . 0 (b) } d d x } [ln ( 2 x ) 1 C ] 5 } 2 1 x } } d d x } ( 2 x ) 5 1 } 2 1 x } 2 ( 2 1) 5 } 1 x } for x , 0 (c) For x . 0, ln ) x ) 1 C 5 ln x 1 C , which is a solution to the differential equation, as we showed in part (a). For x , 0, ln ) x ) 1 C 5 ln ( 2 x ) 1 C , which is a solution to the differential equation, as we showed in part (b). Thus, } d d x } ln ) x ) 5 } 1 x } for all x except 0. (d) For x , 0, we have y 5 ln ( 2 x ) 1 C 2 , which is a solution to the differential equation, as we showed in part (a). For x . 0, we have y 5 ln x 1 C 1 , which is a solution to the differential equation, as we showed part (b). Thus, } d d y x } 5 } 1 x
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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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