How do I formally show that lim x^2 - sin(x) as x tends to infinity is infinity?
I suppose you could look at the minimum possible value of your function... since sin(x) can never be greater than one, your equation can never be less than x^2-1. So work with that instead.
There's a theorem that is sometimes called the Squeeze Theorem or Squeeze Play Theorem. If f(x) <= g(x) <= h(x) for all x in a suitable domain, and lim f(x) = lim h(x) = L, then lim g(x) = L.
x^2 - 1 <= x^2 - sin(x) <= x^2 + 1 for all x. What can you say about lim x^2 -1 and lim x^2 + 1 as x grows large without bound?
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