lim(x→1) lncos(x-1)/(1-sin(πx/2))

问题描述:

lim(x→1) lncos(x-1)/(1-sin(πx/2))

原式=lim(x→1) ln[1+cos(x-1)-1]/(1-sin(πx/2))
=lim(x→1) [cos(x-1)-1]/(1-sin(πx/2))
=lim(x→1)[-1/2(x-1)^2]/(1-sin(nx/2)
接下就完全是利用洛比达法则了,鉴于符号太难打了,就不赘述了