用罗比达法则,上下同时求导,即为:lim(e^x-e^(-x))/2x,再次用罗比达法则,上下求导,得,lim(e^x+e^(-x))/2=1,最后答案为1!
lim(x→0)(e^x+e^(-x)-2)/x^2(这是0/0型,运用洛必达法则)=lim(x→0)(e^x-e^(-x))/2x(再运用洛必达法则))=lim(x→0)(e^x+e^(-x))/2=1
=lim(1+x+x^2/2+1-x+x^2/2-2+o(x^2)/x^2=lim(x^2+o(x^2))/x^2=1
1