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calculus TA here, trying to come up with good outside-the-box questions for my students, this one turns out to be subtler and harder than meets the eye-- I can't find a solution which satisfies me, one which isn't too ad hoc!

The problem is: prove, using the formal definition of limits, that $$\lim_{x\to -\infty} x^2+30x-1000=\infty$$

Of course, the $-1000$ is just a red herring. But the 30x term seems to nontrivially complicate the problem a bit.

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    What about $x^2 + 30x = (x + 15)^2 - 15^2$? Is this useful?2012-09-06

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