Wiskunde week 8, antw

Wiskunde week 8, antw - Opgavencollege Wiskunde 1, 12...

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Unformatted text preview: Opgavencollege Wiskunde 1, 12 November 2010 Les 8 Uitwerkingen Opgavencollege Wiskunde 1 Les 8 Uitwerkingen Pag. 1/7 • Opgave 1 a) 2 3 2 ( ) ( 1) '( ) 3 1 f x x x x x f x x = + = + ⇒ = + b) 2 3 2 ( ) ( 1)( 1) ( 1) '( ) 3 1 h y y y y y y y y h y y =- + =- =- ⇒ =- c) 2 2 2 2 2 2 2 2 2 2 2 2 2 ( 3) 2 (2 1) 2 2 6 4 2 2 2 6 2( 3) '( ) ( 3) ( 3) ( 3) ( 3) t t t t t t t t t t G t t t t t + ⋅- + ⋅ +---- +- + - = = = = + + + + d) 1 '( ) 2 2 f q xq q =- ; x wordt hierbij beschouwd als een constante. e) 2 2 1 ' ( ) x e x e y e e e x- = ⋅ + f) 2 2 2 2 2 3 6 3 ( 2) 3 ( 2) 3 3 1 6 ( ) '( ) ( 2) ( 2) 2 ( 2) ( 2) x x x x x x x y x y x x x x x x + + + ⋅ - ⋅ = = = ⇒ = = + + + + + (merk opdat dit alleen geldt voor 2) x ≠ - g) 2 1 1 1 ln ln ln ln(1) ln( 1) ln( 1) 1 ( 1)( 1) ( 1) x x y x x x x x x + + = = = =-- = -- ⇒ - +-- 1 ' 1 y x- =- h) 2 2 2 2 1 1 2 ( ) ln(ln( )) '( ) 2 ln( ) ln( ) h x x h x x x x x x = ⇒ = ⋅ ⋅ = i) 2 2 ln(2 ) 2 ln(2 ) (2 ) x x x x x y x e e = = = 2 2 1 ' (2 ) (2 ln(2 ) 2 2) 2(ln(2 ) 1)(2 ) 2 x x y x x x x x x ⇒ = ⋅ + ⋅ ⋅ = + • Opgave 2 a) 2 ( ) (7) d d x xy y dx dx + + = ( , ) (1,2) 1 2 2 1 ( 2 ) ( 1) ( 1) 2 3 5 3 3 13 raaklijn: 2 ( 1) 5 5 5 x y dy dy y x y dx dx dy dy x y y dx dx dy x y y dx dy y dx x y dy dx y x y x = + + + = + = -- + = - + + = - + = -- = -- ⇒ = - + Opgavencollege Wiskunde 1, 12 November 2010 Les 8 Uitwerkingen Opgavencollege Wiskunde 1 Les 8 Uitwerkingen Pag. 2/7 b) 2 ( ) (ln ) d d y y x dx dx + = ( , ) (1, 1) 1 2 1 (2 1) 1 (2 1) 1 raaklijn : 1 1( 1) x y dy dy y dx dx x dy y dx x dy dx x y dy dx y x y x =- + = + = = + = - + = -- ⇒ = - c) 3 2 ( ) ( 1) d d x xy y dx dx + + =- 2 2 2 ( , ) ( 1,1) 3 1 2 (2 ) (3 ) (3 ) (2 ) 4 raaklijn : 1 4( 1) 4 3 x y dy dy x y x y dx dx dy y x x y dx dy x y dx y x dy dx y x y x = - + ⋅ + ⋅ + ⋅ = + = - +- + = + = -- =- + ⇒ = -- d) Er geldt: ( 29 2 2 2 2 2 2 2 x y xy y xy x y x y x + = ⇔- + = ⇔- = ⇔ = Dus: y x = voor elke x ....
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This note was uploaded on 02/22/2012 for the course ECON 158P taught by Professor Bogers during the Winter '10 term at Universiteit van Amsterdam.

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Wiskunde week 8, antw - Opgavencollege Wiskunde 1, 12...

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