求极限:lim(sinx)^tanx (x趋近于pai/2)

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/10 18:41:30

求极限:lim(sinx)^tanx (x趋近于pai/2)
lim(sinx)^tanx (x趋近于pai/2)
谢谢!

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.

求极限:lim(sinx)^tanx (x趋近于pai/2) lim趋近于0((3+2sinx)*x-3*x)/((tanx)*2)求极限 lim趋近于0((3+2sinx)*x)/((tanx)*2)求极限求极限lim(x趋近于0）(根号下(2+tanx)-根号下（2+sinx))/x^3 lim tanx-sinx/sin^2x x趋近于0,x的极限 x趋近pai／2时[secx-tanx]求极限 lim(sinx)^tanx (x趋向于pai/2) 求lim tanx（sinx-1）=,x趋进于pai/2 lim sinx^x(x趋近于0+)求极限 lim sinx^x(x趋近于0+) 求极限数学题lim x趋近于二分之π ln[x-π/2]/tanx 求极限当x趋近于0时,求极限lim((1+2tanx)^(1/x)),