求极限.lim(x→pi/2)(secx-tanx)“pi”=3.14 那个数学字母打不出来.pi/2在lim下面_数学解答

求极限.lim(x→pi/2)(secx-tanx)
“pi”=3.14 那个数学字母打不出来.pi/2在lim下面

人气：414 ℃　时间：2020-05-14 21:40:29

解答

lim(x→π/2) secx-tanx
=lim(x→π/2) 1/cosx-sinx/cosx
=lim(x→π/2) (1-sinx)/cosx
=lim(x→π/2) [(1-sinx)(1+sinx)]/[cosx(1+sinx)]
=lim(x→π/2) (1-sin²x)/[cosx(1+sinx)]
=lim(x→π/2) cosx/(1+sinx)
=cos(π/2)/[1+sin(π/2)]
=0/(1+1)
=0