极限lim(x->3) 根号下[(x-3)/(x^2-9)]怎么求?

极限lim(x->3) 根号下[(x-3)/(x^2-9)]怎么求?
极限lim(x->3) 根号下[(x-3)/(x^2-9)]怎么求?

极限lim(x->3) 根号下[(x-3)/(x^2-9)]怎么求?
分母因式分解
x^2-9=x^2-3^2=(x-3)(x+3)
原式=(x-3)/[(x-3)(x+3)]=1/(x+3)
所以
lim(x->3) 根号下[(x-3)/(x^2-9)]
=lim(x->3) 根号下(1/(x+3))
=根号(1/(3+3))
=根号(1/6)
=(根号6)/6