lim[ln(1-x)+tanπx/2]/cotπx
=lim ln(1-x)/cotπx+lim tanπx/2/cotπx
=lim sin²πx/[π(1-x)] + lim 2tan²(πx/2)/(1-tan²(πx/2))
=-sin2πx-2+lim2/[1-tan²(πx/2)]
=0-2+0
=-2
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