函数f(x)=(cosx)^(1/x^2)(x不等于0),f(x)=a(x=0时),在x=0处连续,求a.
问题描述：
函数f(x)=(cosx)^(1/x^2)(x不等于0),f(x)=a(x=0时),在x=0处连续,求a.
答
答：x≠0,f(x)=(cosx)^(1/x^2)x=0,f(x)=af(x)在x=0处连续,则有：lim(x→0) (cosx)^(1/x^2)=f(0)=alim(x→0) [1-2sin²(x/2)]^(1/x²)=alim(x→0) [1-2*(x/2)²]^(1/x²)=alim(x→0) [(1-x²/2)^...