lim(n-->+∞)(2n^2-1)/(n^2+n+1)=lim(n-->+∞)[(2n^2-1)/(n^2)]/[(n^2+n+1)/(n^2)]=lim(n-->+∞)[2-1/(n^2)]/[1+(1/n)+1/(n^2)]=2/1=2(lim(n-->+∞)(1/n)=0,lim(n-->+∞)[1/(n^2)]=0)