FUNCIOMES Y LIMITES DE FUNCIONES

ACTIVIDAD 5 FUNCIONES Y LIMITES DE FUNCIONES

1. Sean las funciones f(x) = X2+ 3X- 4 y g(x)= X-1; realice las siguientes operaciones:

a) (f + g) (x)= x2 + 3x -4 + x -1

(f + g) (x)= x2 + 4x -5

b) (f - g) (x)= (x2 + 3x -4) – (x - 1)

(f - g) (x)= x2 + 3x -4 –x +1

(f - g) (x)= x2 + 2x -3

c) (fg) (x)= (x2 + 3x -4) (x - 1)

(fg) (x)= x3 + 3x2 – 4x – x2 – 3x + 4

(fg) (x)= x3 + 2x2 – 7x +4

d) (f/g) (x)= x2 + 3x -4

X -1

(f/g) (x)= x + 4

2. Resolver las siguientes funciones:

i. Dado F(x) = X3 – 5 x2 -4x +20 comprobar que:

1. F(1) =12

F (1)= (1)3 – 5(1)2 – 4(1) + 20

F (1)= 1 – 5 -4 +20

F (1)= 12

2. F(5) =0

F (5) = 53 – 5(5)2 -4(5) + 20

F (5) = 125 – 125 -20 + 20

F (5) =0

3. F(0) = -2 f(3)

F (0) = 03 – 5(0)2 4(0) + 20

F (0) = 0 – 0 – 0 + 20

F (0) = 20

ii. Si F (x) = 4 -2x2 +x4 calcular f(0), f(1), f(-1) , f(2)

F (0) = 4 – 2(0)2 + 04

F (0) = 4 – 0 + 0

F (0) = 4

F (1) = 4 – 2(1)2 + 14

F (1) = 4 – 2 + 1

F (1) = 3

F (-1) = 4 – 2(-1)2 + (-1)4

F (-1) = 4 – 2 + 1

F (-1) = 3

F (2) = 4 – 2(2)2 + 24

F (2) = 4 – 8 + 8

F (2) = 4

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