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Calculus › Section D · Applications of derivatives › Topic D.5

Limits at infinity and horizontal asymptotes

Where does a process end up in the long run? Limits at infinity answer that question exactly, and the answers are the horizontal asymptotes you see on so many rational graphs.

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In this topic

  • The long-run question
  • Limits at infinity and horizontal asymptotes
  • The one fact everything stands on
  • The divide-through technique
  • Worked example: matching degrees
  • The three-degree verdict
  • Worked example: the top wins
  • The negative-side trap
  • Long-run answers in the world
  • Common mistakes to avoid
  • Key takeaways

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