lim(x趋于0)(1-cosx)/[ln(1+x)(e^x-1)]

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/18 12:47:51
lim(x趋于0)(1-cosx)/[ln(1+x)(e^x-1)]lim(x趋于0)(1-cosx)/[ln(1+x)(e^x-1)]lim(x趋于0)(1-cosx)/[ln(1+x)(e^x-1

lim(x趋于0)(1-cosx)/[ln(1+x)(e^x-1)]
lim(x趋于0)(1-cosx)/[ln(1+x)(e^x-1)]

lim(x趋于0)(1-cosx)/[ln(1+x)(e^x-1)]
运用等价无穷小:1-cosx~1/2x^2,ln(1+x)~x,e^x-1)~x
lim(x→0)(1-cosx)/[ln(1+x)(e^x-1)]
=lim(x→0)1/2x^2/x^2
=1/2