limx趋向于0 根号（x+1)-1/x的极限._数学解答

limx趋向于0 根号（x+1)-1/x的极限.

人气：429 ℃　时间：2019-12-11 05:18:29

解答

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