Question

求lim[(根号x^3)-1]/(x-1),x→1的极限

Answer 1

lim[√(x^3)-1]/(x-1),x→1

令√x=a,则

既是求lim[a^3-1]/(a^2-1),a→1

=lim[(a-1)(a^2+a+1)]/[(a+1)(a-1)],a→1

=lim(a^2+a+1)/(a+1),a→1

=3/2