计算极限lim x->0 √ ̄1-x-1/x

问题描述:

计算极限lim x->0 √ ̄1-x-1/x

原式 = x→0 lim [√(1-x) -1] [√(1-x) +1] / { x [√(1-x) +1] }
= x→0 lim [(1-x) -1] / { x [√(1-x) +1] }
= x→0 lim - 1 / [√(1-x) +1]
= - 1/2