搜狗做题网函数极限题目
来源：学生作业帮 编辑：搜狗做题网作业帮 分类：数学作业 时间：2024/04/28 01:35:07
函数极限题目
lim(xsinx)/(x^2-9)
=lim[(sinx/x)]/[1-(9/x^2)]
=0/(1-0)
=0
lim(sin^2 x-sin^2 T)/(x-T)
=lim(2sinxcosx)/1
=limsin2x
=sin2T
lim(cos√x)^(1/x)=a
===> lna=lim(1/x)ln(cos√x)
===> lna=lim[ln(cos√x)]/x
===> lna=lim[(1/cos√x)*(-sin√x)*(1/2)*(1/√x)]/1
===> lna=lim(-1/2)*tan√x/√x
===> lna=lim-1/2
===> a=e^(-1/2)
即,原式=e^(-1/2)
limxsin(4/x)
=limsin(4/x)/(1/x)
=lim4*[sin(4/x)/(4/x)]
=4*1
=4
=lim[(sinx/x)]/[1-(9/x^2)]
=0/(1-0)
=0
lim(sin^2 x-sin^2 T)/(x-T)
=lim(2sinxcosx)/1
=limsin2x
=sin2T
lim(cos√x)^(1/x)=a
===> lna=lim(1/x)ln(cos√x)
===> lna=lim[ln(cos√x)]/x
===> lna=lim[(1/cos√x)*(-sin√x)*(1/2)*(1/√x)]/1
===> lna=lim(-1/2)*tan√x/√x
===> lna=lim-1/2
===> a=e^(-1/2)
即,原式=e^(-1/2)
limxsin(4/x)
=limsin(4/x)/(1/x)
=lim4*[sin(4/x)/(4/x)]
=4*1
=4