Calculo 1

REVIS~AO PARA A PROVA 1 - CALCULO I - Resolvido
1. Seja f (x) = x + 6 p 7 x
.
(a) Determine o domnio desta func~ao.
7 x > 0 =) D(f) = fx 2 R j x < 7g
(b) Calcule f (6) ; f (0) e f (6). f (6) =
(6) + 6 p 7 (6)
= 0 ) f (6) = 0 f (0) =
0 + 6 p 7 0
=
6 p 7
=
6 p 7
7 ) f (0) =
6
p
7
7 f (6) =
6 + 6 p 7 6
=
12 p 7
=
12 p 7
7 ) f (6) =
12
p
7
7
2. f (x) e a func~ao denida por f (x) = 6x + 2.
(a) Determine a raiz e os coecientes linear e angular.
Raiz: f (x) = 0 =) 6x + 2 = 0 =) 6x = 2 =) x = 2
6
= 3 =) A raiz e x = 3 coe ciente angular = 6 coeciente linear = 2
(b) Diga se a func~ao e crescente ou decrescente.
Decrescente, porque o coeciente angular e negativo.
(c) Os pontos P (2;10) e Q(1; 5) s~ao pontos do graco de f (x)? f (2) = 6  2 + 2 = 10 =) P (2;10) e ponto do graco f (1) = 6 (1) + 2 = 8 6= 5 =) Q(1; 5) n~ao e ponto do graco
3. Sejam f (x) = 3x2 + 1 e g (x) = 2x + 3.
(a) Verique se as func~oes s~ao pares ou mpares. f (x) = 3x2 + 1 = f (x) ) f (x) e par f (x) = 3x2 1 6= f (x) ) f (x) n~ao e mpar g (x) = 2x + 3 6= g (x) ) g (x) n~ao e par g (x) = 2x 3 6= g (x) ) g (x) n~ao e mpar
(b) Determine f (x)  g (x) ; (f  g) (x) ; (g  f) (x) ; (f  f) (x) e (g  g) (x). f (x)  g (x) =

3x2 + 1


 (2x + 3) = 6x3 + 9x2 + 2x + 3 ) f (x)  g (x) = 6x3 + 9x2 + 2x + 3
(f  g) (x) = f (g (x)) = f (2x + 3) = 3 (2x + 3)2 + 1 = 3

4x2 + 12x + 9


+ 1
= 12x2 + 36x + 27 + 1 = 12x2 + 36x + 28 ) (f  g) (x) = 12x2 + 36x + 28
(g  f) (x) = g (f (x)) = g

3x2 + 1


= 2

3x2 + 1


+ 3 = 6x2 + 2 + 3 = 6x2 + 5 ) (g  f) (x) = 6x2 + 5
(f  f) (x) = f (f (x)) = f

3x2 + 1


= 3

3x2 + 1

2 + 1 = 3

9x4 + 6x2 + 1


+ 1
= 27x4 + 18x2 + 3 + 1 = 27x4 + 18x2 + 4 ) (f  f) (x) = 27x4 + 18x2 + 4
(g  g) (x) = g (g (x)) = g (2x + 3) = 2 (2x + 3) + 3 = 4x + 6 + 3 = 4x + 9 ) (g  g) (x) = 4x + 9
(c) Determine (f  g) (0) ; (g  f) (1) ; (f  f) (1) e (g  g) (2).