Find the limit of (x^2+x)^(1/2)-x as x approaches -infinity

 Exercise

$\lim_{x\to-\infty}\left(\sqrt{x^2+x}-x\right)$

 

Evaluate the limit $\lim_{x\to{- \infty }}\left(\sqrt{x^2+x}-x\right)$ by replacing all occurrences of $x$ by $- \infty $

$\sqrt{\left(- \infty \right)^2- \infty }+\infty $

 

Simplify $\left(- \infty \right)^2$

$\sqrt{\infty ^2- \infty }+\infty $

 

Infinity to the power of any positive number is equal to infinity, so $\infty ^2=\infty$

$\sqrt{\infty - \infty }+\infty $

 

Infinity minus infinity is an indeterminate form

indeterminate

indeterminate

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.