Ejemplos de funciones

fx=2x4+6x2-3x-1
Encontrar f(x+3)±f(x+1)
fx+3=2(x+3)4+6(x+3)2-3(x+3)-1=2x4+4x33+6x2(3)2+4x(3)3+(3)4+6x2+2x3+(3)2-3x-9-1
=2x4+8x3+24x3+108x2+144x+243+6x2+36x+9-3x-9-1
=2x4+32x3+114x2+177x+242fx+1=2(x+1)4+6(x+1)2-3(x+1)-1
=2x4+4x31+6x2(1)2+4x13+(1)4+6x2+2x1+(1)2-3x+3-12x4+8x3+12x2+8x+1+6x2+12x+1-3x+3-1
= 2x4+8x3+18x2+17x+2
fx+3+fx+1= 2x4+32x3+114x2+177x+242+2x4+8x3+18x2+17x+2=4x4+40x3+232x2+194x+244
fx+3-fx+1= 2x4+32x3+114x2+177x+242-2x4+8x3+18x2+17x+2
=26x3+87x2+160x+240

Si fx=12x5 demostrarque fx+h-fx÷h=60x4 cuando h→0
fx+h=12x+h5
=12x5+5x4h+10x3h2+10x2h3+5xh4+h5=12x5+60x4h+120x3h2+120x2h3+60xh4+12h5
fx+h-fx÷h=12x5+60x4h+120x3h2+120x2h3+60xh4+12h5÷h
=60x4+120x3h+120x2h2+60xh3+12h4cuando h→0
=60x4

si fx=3x4demostrar que fx+h-fx÷h=-12x5cuando h→0
fx+h=3x+h4=33x4+4x3h+6x2h2+4xh3+h4fx+h-fx÷h=33x4+4x3h+6x2h2+4xh3+h4-3x4÷h
=4x3+6x2h+4xh2+h3 cuando h→0
=4x3=-12x5

si fx=x+2determinar que fx+h-fx÷h=1x+2cuando h→0
fx+h=x+h+2=x+h+2
fx+h-fx÷h=x+h+2-x+2 ÷h cuando h→0
=1x+2