Tentamen jan 2009 uitwerkingen

Tentamen jan 2009 uitwerkingen - Uitwerkingen tentamen...

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Uitwerkingen tentamen 9-1-2009 Opgave 1 ) ( x f = 2 2 ) 4 ( 4 + x x a. () 1 fx = 2 2 4 1 (4 ) x x = + 4 x ≠− 22 4( 4 xx =+ ) ( ) 24 o f 2 x x 4 = += + 4 of 4. 3 =− = Of: = 2 2 4 1 ) x x = + 4 x 4 ) 1 6 48 x = ++ 2 38 1 6 −+ + = 0 4 of 4. 3 = b. Verticale asymptoot: noemer = 0 0 ) 4 ( 2 = + x 0 4 = + x 4 = x (teller 0). ) ( lim x f x ± = 2 2 ) 4 ( 4 lim + ± x x x = 16 8 4 lim 2 2 + + ± x x x x = 2 2 4 lim x x x ± = 4. Horizontale asymptoot: . 4 = y c. = ) ( x f 2 2 ) 4 ( 4 + x x ) ( x f = 4 2 2 ) 4 ( 1 ) 4 ( 2 4 8 ) 4 ( + + + x x x x x = 2 4 ) ) 8 8 ) x x x + = 3 2 ) 4 ( 8 8 ) 4 ( + + x x x x = 3 2 2 ) 4 ( 8 32 8 + + x x x x = 3 ) 4 ( 32 + x x . 0 ) ( = x f 0 ) 4 ( 32 3 = + x x 0 32 = x 0 = x . Tekenoverzicht van f 0 4 0 + + + × + + + Minimum bij 0 = x , y = = ) 0 ( f 2 2 ) 4 0 ( 0 4 + = 0. d. = ) ( x f 3 ) 4 ( 32 + x x ) ( x f = 6 2 3 ) 4 ( 1 ) 4 ( 3 32 32 ) 4 ( + + + x x x x = [ ] 2 6 ( 4) ( 4) 32 96 ) x x + = 4 ) 4 ( 96 32 ) 4 ( + + x x x = 4 ) 4 ( 96 128 32 + + x x x = 4 ) 4 ( 128 64 + + x x . e. 0 ) ( = x f 0 ) 4 ( 128 64 4 = + + x x 0 128 64 = + x 128 64 = x . 2 = x Buigpunt bij , y = = 2 = x ) 2 ( f 2 2 ) 4 2 ( 2 4 + = 36 16 = 9 4 .
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Tentamen jan 2009 uitwerkingen - Uitwerkingen tentamen...

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