Question

求x→1时lim（2-x）^tan（πx）/2的极限（能不能不用若必达法则）,

Answer 1

y=(2-x)^tan(πx/2)=[(1+1-x)^(1/(1-x))]^[tan(πx/2)*(1-x)

x→1时,底数[1+1-x)^(1/(1-x))]趋于e

指数:

limtan(πx/2)*(1-x)=limsin(πx/2)(1-x)/(cos(πx/2)

=lim(1-x)/(cos(πx/2)=lim(1-x)/(π/2)(1-x)=2/π