Why \begin{equation} \lim_{x\to-\infty}\sqrt{x^2-x-1}-x=+\infty, \end{equation} Thanks
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What have you tried so far? Can you try and roughly graph the function and tell me what you think happens when $x \to \infty$? – Siddharth Bhat Apr 27 '16 at 09:28
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@Claude Leibovici The duplicate is to $\infty$, this one is to $-\infty$. That makes the question different and considerably easier. – wythagoras Apr 27 '16 at 09:57
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thank you for your answers. I have clear ideas – ChercheFind Apr 27 '16 at 10:26
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It is enough to notice that $\sqrt{t} > 0$ for all $t$. So $\sqrt{x^2-x-1} > 0$ and hence $\sqrt{x^2-x-1} -x > -x$, and the latter goes to infinity if $x$ goes to $-\infty$.
wythagoras
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