lim(x→1)lncos(x-1)/(1-sin(πx/2))詳細過程

lim(x→1)lncos(x-1)/(1-sin(πx/2))詳細過程

lim(x→1)lncos(x-1)/(1-sin(πx/2))
令x-1=t,t→0
原式=lim(t→0)lncost/(1-sin(π(t+1)/2))
=lim(t→0)lncost/(1-cos(πt/2))
=lim(t→0)-sint/cost/(π/2*sin(πt/2))
=-2/πlim(t→0)sint/sin(πt/2)
=-2/π*2/π
=4/π^2