极限微分的真问题

lim[(x+h)^3 - x^3]/h

=lim[3x^2？+ 3x * h^2 + h^3]/h

=lim[3x^2 + 3x * h + h^2]

=lim(3x^2)+lim(3x h)+lim(h)^2

=3x^2 + lim(3x * 0) + lim(0)^2

=3x^2

=lim(1+u^3)^(1/4)/(1+u)

=lim[(1+u^3)/(1+u)^4]^(1/4)

= lim[(1+u)(1-u+u^2)/(1+u)^4]^(1/4)

=lim[(1-u+u^2)/(1+u)^3]^(1/4)

=lim[(1-u+u^2)/(1+3u+3u^2+u^3)]^(1/4)

= lim {[(1/u)3-(1/u)2+(1/u)]/[(1/u)3+3 *(1/u)

=lim[(0^3-0^2+0)/(0^3+3*0^2+3 * 0+1)]^(1/4)

=lim[0/1]^(1/4)

=0