Question

文科高等数学之求极限问题lim [(根号x^2+x+1)-(根号x^2-x+1)]x->+∞

Answer 1

原式=lim[√(x^2+x+1)-√(x^2-x+1)][√(x^2+x+1)+√(x^2-x+1)]/[√(x^2+x+1)+√(x^2-x+1)]

=lim[(x^2+x+1)-(x^2-x+1)]/[√(x^2+x+1)+√(x^2-x+1)]

=lim2x/[√(x^2+x+1)+√(x^2-x+1)]

上下除以x

=lim2/[√(1+1/x+1/x^2)+√(1-1/x+1/x^2)]

=2/(√1+√1)

=1