lim 根号（6－x）－2

原式=(x->2)lim{[√(6-x)-2][√(6-x)+2][√(3-x)+1]/
/[√(3-x)-1][√(3-x)+1][√(6-x)+2]}
=(x->2)lim{(6-x-4)[√(3-x)+1]/(3-x-1)[√(6-x)+2]}
=(x->2)lim{(2-x)[√(3-x)+1]/(2-x)[√(6-x)+2]}
=(x->2)lim{[√(3-x)+1]/[√(6-x)+2]}
=[√(3-2)+1]/[√(6-2)+2]
=(1+1)/(2+2)
=1/2.
另一解法：
原式=(x->2)lim{[-1/(2√(6-x))]/[-1/(2√(3-x))]} (用一次罗比达法则)
=(x->2)lim[√(3-x)/√(6-x)]
=√(3-2)/√(6-2)
=1/2.