Explain whether the statement is true and give an explanation or a counterexample:

Question

If lim f(x) = ∞ and lim g(x) = ∞ , then lim (f(x)-g(x)) = 0.
x->∞ x->∞ x->∞

I think the answer is false, but I'm not sure how to go about explaining why.

Answer 1

∞-∞ is undefined
consider
x^3-x^2 --> ∞
time to read up on limits and infinity. It's a tricky subject.