limx趋于1 sin兀x/1-x^2

limx趋于1 sin兀x/1-x^2

令x-1=t
x=t+1
原式=lim(t->0) sinπ(t+1)/[1-(t+1)^2]
=lim(t->0) -sinπt/[-2t-t^2]
=lim(t->0) (πt)/(2t)
=π/2