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Dominio todos los reales: -∞ < x < ∞
Rango todos los reales: -∞ < x < ∞
Por lo tanto es continua.
X^(1/3) = Y; X = Y³; Inversa = X³
limite no tiene un valor limite.
d/dx(X^1/3) = [X^((1/3) - 1)]/3 ==> [X^(-2/3)]/3 = 1/[3X^(2/3)]
d/dx(X^1/3) = 1/[3X^(2/3)]
Te adjunto una imagen con la grafica.