Ecuaciones

Problema No. 1

a) -1< 3-74 < 6

b)

Solución:

4 (-1) < 4 3-7y < 6 (4)
4

- 4 < 3-7y y > -3

Ordenando:

-3 < y 0 (-∞,-1) u (-1 ,1)u (1, ∞)

x2 1>0 + 1

x2 >1

x > 1

x > + 1

c) f (x)= 2x3 +x2

2x-3 ≥0

2x ≥0+3

2x≥3

2x≥3/2

Problema No. 6

a) f (x)= x
x2 - 4Solución:

1. y+[pic]y= f (x+[pic]x)

y+[pic]y= f x+[pic]x

(x+[pic] x)2-4

2. y +[pic]y= x+[pic]x

(x+[pic] x)2-4

y= xx2- 4

[pic]y = x+[pic]x - x
x2- 4 x2-4

[pic]y = (x2 - 4) ( x+[pic]x ) - x [(x+∆x)2- 4]
[(x+∆x)2-4][ x2-4][pic]y = x3 + x2 [pic]x - 4 x - 4∆x-x (x2+2x∆x+(∆x2)- 4)
[(x+∆x)2-4] [ x2-4]

[pic]y = x3 + x2 [pic]x - 4 x - 4∆x-x3 - 2x2∆x-x(∆x2) +4x[(x+∆x)2-4] [ x2-4]

[pic]y = - x2 [pic]x - 4∆ x - (∆x)2
[(x+∆x)2-4] [ x2-4]

[pic]y = - ∆ x (x2 [pic]4 + x ∆ x)
[(x+∆x)2-4] [ x2-4]

3.
[pic]y = -∆ x (x2 [pic]4 + x ∆ x)
∆x [(x+∆x)2-4] [ x2-4]

[pic]y = - (x2 [pic]4 + x ∆ x)
∆x [(x+∆x)2-4] [ x2-4]

4. [pic]y = - [x2 [pic]4 + x (0)]∆x [(x+0)2-4] [ x2-4]

[pic]y = - [x2 [pic]4 ] = - x2 [pic]4
∆x (x2-4) ( x2-4)2

f (x)= 2x-5 + 3xy = 2x-5 + 3x

y+∆y = 2(x+∆x)-5 + 3x (x+∆x)

y+∆y = 2x+2∆x-5 + 3x+3∆x)

- y = 2x-5 - 3x

∆y = 2x+2∆x-5 +3∆x- 2x-5 . 2x+2∆x-5 +3∆x + 2x-5

2x+2∆x-5 +3∆x+ 2x-5

∆y = 2x+2∆x-5 + 3∆x 2 - ( 2x-5)2

2x+2∆x-5 +3∆x+ 2x-5

∆y...