计算lim(x趋向于π/2)(sinx)的tanx次方怎么计算?
来源:学生作业帮 编辑:拍题作业网作业帮 分类:数学作业 时间:2024/03/29 16:47:36
计算lim(x趋向于π/2)(sinx)的tanx次方怎么计算?
解法一:∵lim(x->π/2)[(sinx-1)tanx]
=lim(x->π/2){[(sinx-1)/cosx]sinx}
=lim(x->π/2)[(sinx-1)/cosx]*lim(x->π/2)(sinx)
=lim(x->π/2){[sin(x/2)-cos(x/2)]/[cos(x/2)+sin(x/2)]}*1
=0*1
=0
lim(x->π/2){(sinx)^[1/(sinx-1)]}
=lim(x->π/2){(1+sinx-1)^[1/(sinx-1)]}
=e (应用特殊极限lim(x->0)[(1+x)^(1/x)]=e)
∴原式=lim(x->π/2)[(sinx)^tanx]
=lim(x->π/2)【(sinx)^{[1/(sinx-1)]*[(sinx-1)tanx]}】
=【lim(x->π/2){(sinx)^[1/(sinx-1)]}】^{lim(x->π/2)[(sinx-1)tanx]}
=e^{lim(x->π/2)[(sinx-1)tanx]}
=e^0
=1.
解法二:原式=lim(x->π/2)[(sinx)^tanx]
=lim(x->π/2){e^[tanx*ln(sinx)]}
=e^{lim(x->π/2)[tanx*ln(sinx)]}
=e^{lim(x->π/2)[ln(sinx)/cotx]}
=e^[lim(x->π/2)(-cotx/csc²x)]
=e^[lim(x->π/2)(-sinx*cosx)]
=e^0
=1.
=lim(x->π/2){[(sinx-1)/cosx]sinx}
=lim(x->π/2)[(sinx-1)/cosx]*lim(x->π/2)(sinx)
=lim(x->π/2){[sin(x/2)-cos(x/2)]/[cos(x/2)+sin(x/2)]}*1
=0*1
=0
lim(x->π/2){(sinx)^[1/(sinx-1)]}
=lim(x->π/2){(1+sinx-1)^[1/(sinx-1)]}
=e (应用特殊极限lim(x->0)[(1+x)^(1/x)]=e)
∴原式=lim(x->π/2)[(sinx)^tanx]
=lim(x->π/2)【(sinx)^{[1/(sinx-1)]*[(sinx-1)tanx]}】
=【lim(x->π/2){(sinx)^[1/(sinx-1)]}】^{lim(x->π/2)[(sinx-1)tanx]}
=e^{lim(x->π/2)[(sinx-1)tanx]}
=e^0
=1.
解法二:原式=lim(x->π/2)[(sinx)^tanx]
=lim(x->π/2){e^[tanx*ln(sinx)]}
=e^{lim(x->π/2)[tanx*ln(sinx)]}
=e^{lim(x->π/2)[ln(sinx)/cotx]}
=e^[lim(x->π/2)(-cotx/csc²x)]
=e^[lim(x->π/2)(-sinx*cosx)]
=e^0
=1.
计算lim(x趋向于π/2)(sinx)的tanx次方怎么计算?
计算lim(x趋向于π/2)(sinx)^tanx怎么计算?
lim(sinx)^tanx (x趋向于pai/2)
1、lim(tanx-sinx)/x的立方.x趋向0,2、lim{(2-x)/2}的2/x-1次方.x趋向0,3、lim
利用等价无穷小的性质计算lim(x趋向0) tanx-sinx/sin立方x的极限
求lim x趋向于0(x-sinx)/tanx^3
lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2)) 求极限,
计算极限n趋向于0,lim(x+e^2x)^(1/sinx)
那位数学高手lim(x趋向于π/2){in(sinx)}/(π-2x)^2怎么变成lim(x趋向于π/2){sinx-1
求极限:lim(x趋向于0)(sinx-tanx)/x=?它和lim(sinx+tanx)/x有区别吗?
lim(x趋向于0)(根号1+tanx -根号1+sinx)/(x根号(1+sin^2x) -1)
lim x趋近于无穷大 sin3次方x分之tanx-sinx的极限