$\lim_{x \to \infty}\sqrt{x^2+x}+2\sqrt{x^2+2x}-x$
I tried multiply the conjugate and can't work out. Please advise
2026-04-09 04:02:57.1775707377
Limit tends to infinity $\lim_{x \to \infty}\sqrt{x^2+x}+2\sqrt{x^2+2x}-x$
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It blows up: the first term is larger than $x$, and the second is larger than $2x$, so the whole thing is larger than $3x-x=2x$. (The lesson here is not to get so bound up in technique that you forget to think about what’s actually going on!)