lim→0+ lnx ln(1+X)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/26 03:51:00
lim→0+ lnx ln(1+X)

lim→0+ lnx ln(1+X)
lim→0+ lnx ln(1+X)

lim→0+ lnx ln(1+X)
lim→0+ lnx ln(1+X)
=lim→0+ ln(1+X)/(1/inx) 运用洛比达法则
=lim→0+ (1/x+1)/(-1/xln^2x)
=lim→0+ 1/x+1 *lim→0+ -x*ln^2x
=lim→0+ -ln^2x/(1/x) 运用洛比达法则
=lim→0+ -(2lnx/x)/(-1/x^2)
=lim→0+ 2lnx/(1/x) 运用洛比达法则
=lim→0+ 2/x/(-1/x^2)
=lim→0+ -2x
=0
欢迎追问!