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Question

limx11x2sinπx


Solution

limx11x2sinπx

=limx1(1x)(1+x)sinπx

x1,x10, let x1=yy0

=limy0(y)(1+y+1)sinπ(y+1)

=limy0y(y+2)sin(πy+π)

=limy0y(y+2)sinπy

=limy0y(y+2)sinπy2

=limy0y(y+2)limy0sin πyπy×πy=2π

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