求x→∞时的极限:〔(x²+x+1)½-(x²-x+1)½〕

问题描述:

求x→∞时的极限:〔(x²+x+1)½-(x²-x+1)½〕

=lim(x→∞)2x/〔(x²+x+1)½+(x²-x+1)½〕
=lim(x→∞)2/〔(1+1/x+1/x²)½+(1-1/x+1/x²)½〕
=2/(1+1)=1