Question

lim(根号下(x^2+x+1)-根号下(x^2-x+1))x趋向于正无穷求极限详细过程

Answer 1

分子有理化,上下乘√(x^2+x+1)+√(x^2-x+1)

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

=2x/[√(x^2+x+1)+√(x^2-x+1)]

上下除x

=2/[√(1+1/x+1/x^2)+(1-1/x+1/x^2)]

x在分母的都趋于0

‘所以极限=2/(1+1)=1