- #1

farleyknight

- 146

- 0

## Homework Statement

[itex]\lim_{x \to -\infty} x + \sqrt{x^2 + 6x}[/itex]

## Homework Equations

## The Attempt at a Solution

Previous attempt was guessing it was [itex]\infty[/itex], but I see now my flaw and the actual answer is -3. Somewhere else on the web, might have been this forum, it was said that one could flip the sign and get

[itex]\lim_{x \to -\infty} x + \sqrt{x^2 + 6x} = \lim_{x \to \infty} -x + \sqrt{x^2 + 6x}[/itex]

Which I can see intuitively, since the what is under the radical would be positive either way, which implies that the sign only need be flipped for x. However, is there a generalized proof that includes any number of polynomials and roots, for this fact?

Thanks,

- Farley