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.