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3.6 Worksheet Answers Part II 1. 10 ln 1 10 ln 1 1 1 1 log ) ( - = - = - = x f x f x x x f 2. ( 29 ( 29 ( 29 -  - + - - = - + = 2 ln 1 1 ln 1 1 ln 1 ln 1 ln 1 ) ( t t t t t f t t t f ( 29 2 ln 1 ln 1 ln 1 t t t t f - + + - = ( 29 2 ln 1 2 t t f - = 3. + + + + = + = ) 1 ( ) 1 ( 1 ) 1 ln( ) 1 ln( ) ( y y y y e dy d e y e F e y y F ( 29 ( 29 y y y e ye e F + + + = 1 1 ln 4. ( 29 ( 29 + = + = 10 2 2 1 10 2 1 ln ln 1 2 2 x e x y x e x y x x ( 29 1 ln 10 ln ln 2 1 ln 2 2 + + + = x e x y x ( 29 1 ln 10 ln 2 1 ln 2 2 + + + = x x x y ( 29 1 1 10 2 2 1 1 2 2 + + + + = x dx d x x x dx dy y ( 29 ( 29 ( 29 + + + + + + = + + + = 1 2 40 1 2 1 1 1 20 2 2 1 2 2 2 2 10 2 2 2 x x x x x x x e x dx dy x x x x y dx dy x ( 29 [ ] x x x x x e dx dy x 2 1 2 41 2 1 2 3 9 2 2 + + + + = Math 151 Page 1

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5. ( 29 ( 29 [ ] ) ln(sin ln sin ln ln sin x x y x y x y x x = = = ( 29 ( 29 ( 29 + = + = x x x x y dx dy x dx d x x x dx dy y sin cos sin ln sin sin sin ln 1 ( 29 ( 29 [ ] x x x x dx dy x cot sin ln sin + = 6. ( 29 x x x x dx dy y x x y x y x y x x ln 1 ln 1 1 ln ln ln ln ln ln ln + = = = = x x dx dy x x x dx dy x x y dx dy x
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