Question

How to solve this question?

Answer 1

[tex] \lim_{x \to \infty} (x - \sqrt{x^2+x+1} ) = \lim_{y \to 0} ( \frac{1}{y} - \frac{\sqrt{y^2+y+1}}{y} ) = \\ = \lim_{y \to 0} \frac{1-\sqrt{y^2+y+1}}{y} [/tex]
now apply l hospital's rule 0/0
 $lim_{y \to 0} \frac{-2y-1}{2\sqrt{y^2+y+1}} = \frac{-1}{2}$