Question

怎么求极限？

Answer 1

Answer 2

lim(x->a+) √(x-a)/ √(x^3-a^3)
=lim(x->a+) 1/ √(x^2+ax+a^2)
=√3/(3a)
lim(x->a+) [ √x- √a ]/ √(x^3-a^3)
有理化分子
=lim(x->a+) (x- a)/ [√(x^3-a^3) .(√x+√a) ]
=[1/(2√a)] lim(x->a+) (x- a)/ √(x^3-a^3)
=[1/(2√a)] lim(x->a+) √(x- a)/ √(x^2+ax+a^2)
=0
//
lim(x->a+) [ √x- √a +√(x-a) ]/ √(x^3-a^3)
=lim(x->a+) [ √x- √a ]/ √(x^3-a^3) + lim(x->a+) √(x-a) / √(x^3-a^3)
= 0 +√3/(3a)
=√3/(3a)