# How do you find the limit of sqrt(x^2+2x)+x as x approaches infinity?

We want ${\lim}_{x \rightarrow \infty} \sqrt{{x}^{2} + 2 x} + x$
Both ${x}^{2}$ and $x$ (and therefore $2 x$) increase without bound as $x$ increases, hence $\sqrt{{x}^{2} + 2 x}$ also increases without bound and the limit diverges.