Question

lim(x趋向＋∞)［根号(x＋1)-根号x］怎么求

Answer 1

limx->+∞ [√(x+1)-√x]

=limx->+∞ [√(x+1)-√x][√(x+1)+√x]/[√(x+1)+√x]

=limx->+∞(x+1-x)/[√(x+1)+√x]

=limx->+∞ 1/[√(x+1)+√x]

=limx->+∞ 1/√x[√(1+1/x) +1]

=limx->+∞ 1/√x *limx->+∞ 1/[√(1+1/x) +1]

=0*1/[(1+0)+1]

=0