当x趋近于1时((1–x)tan2/兀x)得极限

Question

当x趋近于1时((1–x)tan2/兀x)得极限

Answer 1

令1-x=t
原式=lim(t->0) t/tan(π/2 (1-t))
=lim(t->0) t/tan(π/2 -π/2t))
=lim(t->0) t/cot(πt/2)
=lim(t->0) t×tan(πt/2)
=0*0
=0