lista4 - 1 Quarta lista de exerccios 1. Para cada funo f...

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Quarta lista de exercícios 1. Para cada função f dada, calcule a derivada indicada: a ) ; 2 5 3 6 ) ( 4 5 + = x x x x f 25 25 dx y d . b ) ; . c ) x x f sen ) ( = ) ( ) 37 ( x f x x f 1 ) ( = ; n n dx y d . 2. Determine a derivada de ordem n de y = ln x . 3. Derive: a ) y = arctg (arcsen x ). b ) y = ln(sec x + tg x ). c ) . x x y = d ) y = arcsen 2 1 x . e ) y = arcsen (e 2 x – 1). 4. Determine para quais valores de x cada função a seguir está definida: a ) y = arcsen(2 x + 1) b ) y = arccos(e x 5) c ) y = arctg(3 x + 2) 5. Determine os intervalos de crescimento e decrescimento de cada função a seguir. a ) y = 3 x 4 16 x 3 + 18 x 2 . b ) y = x 3 3 x 2 + 1. 6. Determine os pontos críticos de cada função a seguir: a ) y = x 3 + x 2 – x. b ) 1 1 ) ( 2 + + + = x x x x f . c ) 3 2 x y = . d ) 5 2 x y = . Respostas: 1) a ) . 0 25 25 = dx y d b ) c ) . cos ) ( ) 37 ( x x f = ( ) . ! 1 1 + = n n n n x n dx y d 2) ()( ) . ! 1 1 ln 1 n n n n x n dx x d = 3) a ) . 1 1 arcsen 1 1 2 2 x x dx dy + = b ) . sec x dx dy = c ) ( . ln 1 x x dx dy x + = ) d ) < > = = . 0 1 1 0 1 1 1 | | 2 2 2 x se x x se x x x x dx dy e ) () . 1 e - 1 e 2 2 2x 2 = x dx dy 4) a ) . 0 1 x b ) . 6 ln 4 ln x c ) . < < x 5) a ) cresce para e 1 0 < < x < < x 3 ; decresce para 0 < < x e . 3 1 < < x b ) cresce para e 0 < < x < < x 2 ; decresce para
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This note was uploaded on 10/30/2011 for the course ECON 101 taught by Professor Vários during the Spring '11 term at Universidade Federal do Rio de Janeiro.

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lista4 - 1 Quarta lista de exerccios 1. Para cada funo f...

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