Lim cuando x tiende a 2 x^3-8/x-2
Lim cuando x tiende a 9 x^4-81/x^2-9
Lim cuando x tiende a 4 x^2-2x-8/x^2+2x-24
Muestre que el valor de x^2-x-6/x^2-7x+12 es cercano a -5 si x es cercano a 3
Hola
1)
diferencia de cubos
x^3 - 8 = (x - 2) (x^2 + 2 x + 4)
Entonces
Lim(x^3-8)/(x-2) = Lim(x^2 + 2 x + 4) = 4+4+4 = 12
..x->2.....................x->2
2)
Diferencia de cuadrados
x^4 - 81 = (x^2)^2 - (9)^2 = (x^2 - 9) (x^2 + 9)
Lim(x^4 - 81)/(x^2 - 9) = Lim(x^2 + 9) = 9+9 = 18
..x->3..............................x->3
3)
buscamos los factores (x - 4)
x^2 - 2 x - 8 = x^2 - 4 x + 2 x - 8 = x(x - 4) + 2(x - 4) = (x + 2)(x -4)
x^2 + 2 x - 24 = x^2 - 4 x + 6 x - 24 = x(x - 4) + 6(x - 4) = (x + 6)(x -4)
Lim(x^2 - 2 x - 8)/(x^2 + 2 x - 24) = Lim(x+2)/(x+6) = 6/10 = 3/5
..x->4..................................................x->4
4)
buscamos los factores de (x - 3)
x^2 - x - 6 = x^2 - 3 x + 2 x - 6 = x(x - 3) + 2(x - 3) = (x+2)(x-3)
x^2 - 7x - 12 = x^2 - 3 x - 4 x + 12 = x(x - 3) - 4(x - 3) = (x-4)(x-3)
Lim(x^2 - x - 6)/(x^2 - 7x - 12) = Lim(x+2)/(x-4) = 5/1 = 5
..x->3..................................................x->3
Saludos
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Answers & Comments
Hola
1)
diferencia de cubos
x^3 - 8 = (x - 2) (x^2 + 2 x + 4)
Entonces
Lim(x^3-8)/(x-2) = Lim(x^2 + 2 x + 4) = 4+4+4 = 12
..x->2.....................x->2
2)
Diferencia de cuadrados
x^4 - 81 = (x^2)^2 - (9)^2 = (x^2 - 9) (x^2 + 9)
Lim(x^4 - 81)/(x^2 - 9) = Lim(x^2 + 9) = 9+9 = 18
..x->3..............................x->3
3)
buscamos los factores (x - 4)
x^2 - 2 x - 8 = x^2 - 4 x + 2 x - 8 = x(x - 4) + 2(x - 4) = (x + 2)(x -4)
x^2 + 2 x - 24 = x^2 - 4 x + 6 x - 24 = x(x - 4) + 6(x - 4) = (x + 6)(x -4)
Lim(x^2 - 2 x - 8)/(x^2 + 2 x - 24) = Lim(x+2)/(x+6) = 6/10 = 3/5
..x->4..................................................x->4
4)
buscamos los factores de (x - 3)
x^2 - x - 6 = x^2 - 3 x + 2 x - 6 = x(x - 3) + 2(x - 3) = (x+2)(x-3)
x^2 - 7x - 12 = x^2 - 3 x - 4 x + 12 = x(x - 3) - 4(x - 3) = (x-4)(x-3)
Lim(x^2 - x - 6)/(x^2 - 7x - 12) = Lim(x+2)/(x-4) = 5/1 = 5
..x->3..................................................x->3
Saludos