Variedades Linguisticas

HOJA DE TRABAJO N° 01
1. Dada la función fx=-3x3+2x2+5 , exprese:
fx+h-fxh , fx-h-fxh , fx+h-fx-h2h , En su forma más simple.

a) fx+h-fxh -3x+h3+2x+h2+5-(-3x3+2x2+5)h

-3x3+3x2h+3xh2+h3+2x2+2xh+h2+5+3x3-2x2-5h

-3x3-9x2h-9xh2-3h3+2x2+4xh+2h2+5+3x3-2x2-5h

-9x2h-9xh2-3h3+4xh+2h2h

h(-9x2-9xh-3h2+4x+2h)h

-9x2-9xh-3h2+4x+2h

b)fx-h-fxh -3x-h3+2x-h2+5-(-3x3+2x2+5)h

-3x3-3x2h+3xh2-h3+2x2-2xh+h2+5+3x3-2x2-5h

-3x3+9x2h-9xh2+3h3+2x2-4xh+2h2+5+3x3-2x2-5h

9x2h-9xh2+3h3-4xh+2h2h

h(9x2-9xh+3h2-4x+2h)h

9x2-9xh+3h2-4x+2h

c) fx+h-fx-h2h -3x+h3+2x+h2+5-(-3x-h3+2x-h2+5)2h

-3x3+3x2h+3xh2+h3+2x2+2xh+h2+5-(-3x3-3x2h+3xh2-h3+2x2-2xh+h2+5)2h-3x3-9x2h-9xh2-3h3+2x2+4xh+2h2+5-(-3x3+9x2h-9xh2+3h3+2x2-4xh+2h2+5)2h
-3x3-9x2h-9xh2-3h3+2x2+4xh+2h2+5+3x3-9x2h+9xh2-3h3-2x2+4xh-2h2-5)2h

-9x2h-3h3+4xh-9x2h-3h3+4xh)2h

-18x2h-6h3+8xh)2h

2h(-9x2-3h2+4x)2h

-9x2-3h2+4x

2. Dada la función fx=-x2+2x-1 , exprese 13(f2x+f-2x ; 13(fx-f-x en su forma más simple.

a) 13(f2x+f-2x13(-2x2+22x-1+--2x2+22x-1)

13(-4x2+4x-1-4x2-4x-1)

13(-8x2-2)

-8x2-23

b) 13(fx-f-x 13(-x2+2x-1-(--x2+2-x-1))

13(-x2+2x-1-(-x2-2x-1))

13(-x2+2x-1+x2+2x+1))

4x3

3. Dada la función fx=1x2 , calcular f13-f4(f1+f-1)3 .

*) f13-f4(f1+f-1)3 1(13)3-142(112+1-12)3 = 9-116(1+1)3 = 14316(2)3143168 = 143128

4. Dadas las siguientes funciones:

a) fx=x2-5x+4 ; b) fx=x3+3x2+3x+1 ; c) fx=3x3-3x2-1
d) fx=x2(x2+2x+1)

Calcular: f0 , f-t , f-1 , ft , fx+h , fx-h

a) fx=x2-5x+4

** f0 f0=02-5(0)+4 ** f-tf-t=(-t)2-5(-t)+4

f0=4 f-t=t2+5t+4

** f-1 f-1=(-1)2-5(-1)+4 ** ft ft=(t)2-5(t)+4

f-1=10ft=t2-5t+4

** fx+h fx+h=(x+h)2-5(x+h)+4

fx+h=x2+2xh+h2 -5x-5h+4

** fx-h fx-h=(x-h)2-5(x-h)+4

fx-h=x2-2xh+h2 -5x+5h+4

b) fx=x3+3x2+3x+1

** f0 f0=03+3(0)2+3(0)+1** f-t f-t=(-t)3+3(-t)2+3(-t)+1

f0=1 f-t=-t3+3t2-3t+1

** f-1 f-1=(-1)3+3(-1)2+3(-1)+1 ** ft ft=t3+3(t)2+3(t)+1

f-1=0ft=t3+3t2+3t+1

** fx+h fx+h=(x+h)3+3(x+h)2+3(x+h)+1

fx+h=x3+3x2h+3xh2+h3 +3x2+6xh+3h2+3x+3h+1

** fx-h fx-h=(x-h)3+3(x-h)2+3(x-h)+1

fx-h=x3-3x2h+3xh2-h3+3x2-6xh+3h2+3x-3h+1
c) fx=3x3-3x2-1

** f0 f0=3(0)3-302-1 ** f-t f-t=3(-t)3-3(-t)2-1

f0=3 f-t= -3t3-3t2-1

** f-1 f-1=3(-1)3-3(-1)2-1...