A quick question about limits?

Well, if you have a formula and after changing the x's into ∞'s you get (∞+1-∞^2)/∞, what do you exactly get on the numerator? ∞? -∞? Or you get ∞-∞ and you have to find that limit before moving on to ∞/∞?

I would really appreciate a quick answer, anybody out there willing to help me? :)

Update:

I think I didn't explain it the right way lol xD I already knew that ∞-∞ and ∞/∞ are both undetermined forms but in that particular case, ∞+1-∞^2, do you get the undetermined form ∞-∞ or do you just get ∞/-∞ and you move to the outer undeterminated form [(∞+1-∞^2)/∞]?

Thanks anyway! :)

2 Answers

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  • 9 years ago
    Favorite Answer

    Any time we get a limit of infinity/infinity, we must be careful because the limit could turn out to be any real number or +/- infinity. The same is true for infinity - infinity cases as well. In either case, we call these indeterminate forms.

    To First Answerer: Consider f(x)=x/e^x, lim(x-->infinity) f(x) is of form (infinity/infinity), yet by l'hopital's rule d/dx(x)=1 and d/dx(e^x)=e^x, lim(x-->infnity) f(x)= lim(x-->infinity) (1/e^x)=0. Clearly this exists so only true for some limits, not all.

  • Anonymous
    9 years ago

    limit does not exist

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