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Pre-Calc Homework Solutions 29

# Pre-Calc Homework Solutions 29 - Section 1.5 39 e x e x 29...

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39. e x 1 e 2 x 5 3 e x 2 3 1 e 2 x 5 0 e x ( e x 2 3 1 e 2 x ) 5 e x (0) ( e x ) 2 2 3 e x 1 1 5 0 e x 5 e x 5 } 3 6 2 ˇ 5 w } x 5 ln 1 } 3 6 2 ˇ 5 w } 2 < 2 0.96 or 0.96 Graphical support: [ 2 4, 4] by [ 2 4, 8] 40. 2 x 1 2 2 x 5 5 2 x 2 5 1 2 2 x 5 0 2 x (2 x 2 5 1 2 2 x ) 5 2 x (0) (2 x ) 2 2 5(2 x ) 1 1 5 0 2 x 5 2 x 5 } 5 6 2 ˇ 2 w 1 w } x 5 log 2 1 } 5 6 2 ˇ 2 w 1 w } 2 < 2 2.26 or 2.26 Graphical support: [ 2 4, 4] by [ 2 4, 8] 41. ln y 5 2 t 1 4 e ln y 5 e 2 t 1 4 y 5 e 2 t 1 4 42. ln( y 2 1) 2 ln 2 5 x 1 ln x ln( y 2 1) 5 x 1 ln x 1 ln 2 e ln( y 2 1) 5 e x 1 ln x 1 ln 2 y 2 1 5 e x ( x )(2) y 5 2 xe x 1 1 43. y 5 } 1 1 10 2 0 2 x } 1 1 2 2 x 5 } 10 y 0 } 2 2 x 5 } 10 y 0 } 2 1 log 2 (2 2 x ) 5 log 2 1 } 10 y 0 } 2 1 2 2 x 5 log 2 1 } 10 y 0 } 2 1 2 x 5 2 log 2 1 } 10 y 0 } 2 1 2 5 2 log 2 1 } 100 y 2 y } 2 5 log 2 1 } 100 y 2 y } 2 Interchange x and y . y 5 log 2 1 } 100 x 2 x } 2 f 2 1 ( x ) 5 log 2 1 } 100 x 2 x } 2 Verify. ( f + f 2 1 )( x ) 5 f 1 log 2 } 100 x 2 x } 2 5 5 5 5 } x 1 ( 1 1 0 0 0 0 x 2 x ) } 5 } 1 1 0 0 0 0 x } 5 x ( f 2 1 + f )( x ) 5 f 2 1 1 } 1 1 10 2 0 2 x } 2 5 log 2 1 2 5 log 2 1 2 5 log 2 1 } 2 1 2 x } 2 5 log 2 (2 x ) 5 x 100 }}} 100(1 1 2 2 x ) 2 100 } 1 1 10 2 0 2 x } }} 100 2 } 1 1 10 2 0 2 x } 100 }} 1 1 } 100 x 2 x } 100 }}
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