这两道题都适合用对数法求极限。12、( 2 - x )^[ sec(πx/2) ] = y,两边取对数,[ sec(πx/2) ]ln( 2 - x ) = lny;lim x→1ln( 2 - x )/[ cos(πx/2) ] 是 0/0 型,用罗必塔法则,分子、分母分别求导:= lim x→1[-1/( 2 - x ) ]/[ -(π/2)sin(πx/2) ] = 1/(π/2) = 2/π;故 lny =2/π,y = e^(2/π);14、(sinx)^tanx = y,tanxln(sinx) = lny,sinxln(sinx)/cosx = lny;lim x→π/2sinxln(sinx)/cosx是 0/0 型,用罗必塔法则,分子、分母分别求导:=lim x→π/2 { cosxln(sinx) + sinx/(sinx) * cosx ]/[ -sinx ] = 0/(-1) = 0;lny = 0,y = 1 。