lim(x->π/2)xtanx/tan3x

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lim(x->π/2)xtanx/tan3xlim(x->π/2)xtanx/tan3xlim(x->π/2)xtanx/tan3x令t=x-π/2,原极限=lim(t-->0)(t+π/2)tan(

lim(x->π/2)xtanx/tan3x
lim(x->π/2)xtanx/tan3x

lim(x->π/2)xtanx/tan3x
令t=x-π/2,原极限= lim(t-->0) (t+π/2)tan(3t)/tant= lim(t-->0) (t+π/2)(3t)/t= 3π/2.