Limits at infinity - horizontal asymptotes - Limits

Limits at infinity - horizontal asymptotes

There are times when we want to see how a function behaves near a horizontal asymptote. Much like finding the limit of a function as x approaches a value, we can find the limit of a function as x approaches positive or negative infinity. In this section, we will learn how to evaluate limits at infinity algebraically using the "Highest Power Rule", with tricks like using conjugates, common denominators, and factoring.

Lessons

Notes:
Express all asymptotes in limit notations for the function f whose graph is shown below.
i)limxf(x)=Llim_{x \to\infty } f\left( x \right) = L
ii) limx,f(x)=Llim_{x \to,-\infty } f\left( x \right) = L

horizontal asymptote in limit notation positive infinity

horizontal asymptote in limit notation negative infinity

or

horizontal asymptote in limit notation positive infinity 2

or

horizontal asymptote in limit notation negative infinity 2
  • 1.
    Introduction to Horizontal Asymptotes
  • 4.
    Use "Highest Power Rule" to Evaluate Limits at Infinity of Rational Functions in 3 Types
    Find:
  • 6.
    Multiply Conjugates First, then Evaluate Limits
    Find:
Teacher pug

Limits at infinity - horizontal asymptotes

Don't just watch, practice makes perfect.

We have over 350 practice questions in Calculus for you to master.