Question

lim(x→0)[(1/x)-(1/ln1+x)]

Answer 1

解：
lim【x→0】[1/x-1/ln(1+x)]
=lim【x→0】[ln(1+x)-x]/[xln(1+x)]
=lim【x→0】[1/(1+x)-1]/[ln(1+x)+x/(1+x)]
=lim【x→0】(-x)/[(1+x)ln(1+x)+x]
=lim【x→0】-1/[ln(1+x)+1+1]
=-1/2

答案：-1/2

Answer 2

解：lim(x→0)[(1/x)-(1/ln1+x)]
=lim(x→0){[-x+ln(1+x)]/xln(1+x)}
属于0/0型，运用洛必达法则，=lim(x→0)x/[(x+1)x+ln(1+x)]
属于0/0型，运用洛必达法则=lim(x→0)【1/(3x+2)】=1/2