lim(x→1) lncos(x-1)/(1-sin(πx/2))详细过程

来源:学生作业帮助网 编辑:六六作业网 时间:2025/02/04 07:53:04
lim(x→1)lncos(x-1)/(1-sin(πx/2))详细过程lim(x→1)lncos(x-1)/(1-sin(πx/2))详细过程lim(x→1)lncos(x-1)/(1-sin(πx

lim(x→1) lncos(x-1)/(1-sin(πx/2))详细过程
lim(x→1) lncos(x-1)/(1-sin(πx/2))详细过程

lim(x→1) lncos(x-1)/(1-sin(πx/2))详细过程
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

=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