Wi_VWOBdeel4H15 - Getal en Ruimte VWO B deel 4 hoofdstuk 15...

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Unformatted text preview: Getal en Ruimte VWO B deel 4 hoofdstuk 15 Afgeleide en tweede afgeleide blz.90 1. a. ' e tan ' p P k P y PP rc O OP x p = = = = b. ( ) e '( ) e rc '( ) e x x p k f x f x f p = = = = c. e e e e e e ( 1) 1 rc '( ) e 1 raakpunt ( , e ) (1, e) vergelijking raaklijn: e door e p p p p p p k p k p rc p p p p p f p p p y x b O b y x = = = - = = = = = = + = = 2. a. 2 e 2 rc tan q Q l y A q q + + = = = b. '( ) e '( ) e en rc '( ) e x q q l f x f q f q = = = = Uit a. en b. volgt: e 2 e q q q + = c. 1 2 e 2 ; e Calc intersect geeft: 1,46 x x y y x q x + = = = 3. a. is raaklijn in rc '( ) ( ) ( ) '( ) door tan m m m P f p f p f p f p m O rc O p p = = = = b. 1 1 1 1 e e e ( ) ln '( ) . Gebruik makend van de formule in a. geldt: 1 ln ln 1 e lne 1 (e, 1) rc met door geeft x P m f x x f x p p p y P p p y x b m O b y x = = = = = = = = = + = = blz.93 4. 1 1 2 2 1 2 1 1 4 4 1 4 1 ( ) '( ) 2 ( ) 1 '( ) met ( 4 , 0) geeft: 4 2 4 2 4 2 4 (4,2) (4) 2 1 '( ) '(4) raaklijn: 2 door: (4, 2) 2 1 1 A A B B f x x x f x x x f x y x f x A x x x x x x x x x x B y f f x f y x b x b y x- = = = =-- =- = - + = = + = + = = = = = + = + = + 53 5. a. 2 2 2 2 2 ( ) 1 '( ) 2 ( ) 1 '( ) met (0, 0) geeft: 2 2 1 1 1 1 '( ) 2 (1) 2 door geeft raaklijn: 2 '( ) 2 ( 1) 2 door geeft raaklijn: 2 A A f x x f x x f x y x f x A x x x x x x x x x f x x f O y x f x x f O y x = + =- + = = - = + = = = - = = = = - = - = - b. 2 2 2 2 2 1,2 ( ) 1 '( ) 2 ( ) 1 0 '( ) met (1, 0) geeft: 2 1 2 8 2 2 1 2 1 0 1 2 2 (1 2) 1 2 ; (1 2) 4 2 2 raakpunten: (1 2, 4 2 2) ; (1 2, 4 2 2) A A f x x f x x f x y x f x A x x x x x x x x x x f f = + =- + - = = -- - = + -- = = = + = +- =- + +-- 6. a. Voer in: 1 2 2ln( ) x y x + = en plot (zie figuur hiernaast) 2 2 2 2ln( ) ( ) ; ' 2 ' (2 2ln( )) 1 2 2ln( ) 2ln( ) 2ln( ) '( ) ; '( ) 2ln( ) 1 Zie grafiek: max (1) 2 , 2] x f x f x t n x x t n x x x x f x f x x x x f B + = = = = + = +-- - = = = = = = b. 1 2 1 2 2 2 2 1 2 2 2ln ( ) 2ln( ) 2ln( ) 2 2ln '( ) met (0, 0) geeft: 2ln( ) 2 2ln( ) 4ln( ) 2 ln( ) e Dus rc '(e ) e ; raaklijn: e A A x x f x y x x x f x A x x x x x x x x x x x f y x-- +--- + = = = -- = + = - = - = = = = c. Zie figuur en uitkomst onderdeel b. twee oplossingen voor e a < < 54 7. a. 1 2 2 2 2 1 2 1 2 ( ) (2 1)e '( ) 2 e (2 1)e (2 3)e ( ) (2 1)e '( ) met (0, 0) geeft: (2 3)e (2 3 )e (2 1)e (e 0) 2 3 2 1 2 1 0 geeft: 1 raaklijn 4e ( 4 e ) 1 raakl x x x x x x A A x x x f x x f x x x f x y x f x A x x x x x x x x x x x x x x x y x x x = + = + + = +- + = + = - + = + + = + +- = = = - = = = = - 1 e ijn y x = b....
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This note was uploaded on 11/21/2011 for the course LANGUAGE 201 taught by Professor Hansje during the Winter '00 term at Tilburg University.

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Wi_VWOBdeel4H15 - Getal en Ruimte VWO B deel 4 hoofdstuk 15...

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