当x→0时,1/x-1/ln(x+1)的极限是0吗?求详解

Question

当x→0时,1/x-1/ln(x+1)的极限是0吗?求详解

Answer 1

x→0时,1/x-1/ln(x+1)的极限
=lim【x→0】【ln(x+1)-x】/xln(x+1)
=lim【x→0】【ln(x+1)-x】/x²
=lim【x→0】【1/(x+1)-1】/2x
=lim【x→0】【-x/(x+1)】/2x
=lim【x→0】【-1/2(x+1)】
=-1/2