使用洛必达法则求导 lim(x→pi/2-0):(tanx)^(2x-pi) pi=3.1415926.

lim(x→π/2-0) (tanx)^(2x-π)=e^ lim(x→π/2-0) (2x-π)ln(tanx)=e^ lim(x→π/2-0) ln(tanx)/[1/(2x-π)] ∞/∞型,用罗比达法则=e^ lim(x→π/2-0) 1/(tanx)*sec^2x/[-2/(2x-π)^2] =e^ lim(x→π/2-0) -(2x-π)...=e^ lim(x→π/2-0)1/(tanx)*sec^2x/[-2/(2x-π)^2]=e^ lim(x→π/2-0)-(2x-π)^2/sin(2x)这步是怎么转化的1/(tanx)*sec^2x/[-2/(2x-π)^2]=cosx/sinx*1/(cosx)^2*[-(2x-π)^2]/2=1/(sinxcosx)*[-(2x-π)^2]/2=-(2x-π)^2/(2sinxcosx)=-(2x-π)^2/sin(2x)