lim(x->1/2)sin(1-2x)tanπx
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lim(x->1/2)sin(1-2x)tanπx
lim(x->1/2)sin(1-2x)tanπx
lim(x->1/2)sin(1-2x)tanπx
=lim sin(1--2x)*sin(pix)/cos(pix)=lim sin(1--2x)/cos(pix)=lim 【--2cos(1--2x)】/【--pisin(pix)】
=2/pi.
其中第三个等号用了洛必达法则.
lim(x->1/2)sin(1-2x)/cotπx
=lim(x->1/2)(-2cos(1-2x))/(-πcsc²πx)
=2/π*1/1
=2/π
2/π
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