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Limits at Infinity: Oblique Asymptotes & Horizontal Asymptotes

Explore limits at infinity, oblique asymptotes, horizontal asymptotes, and how to find them using synthetic division. Learn about dividing top and bottom by x to the highest power and checking for radical or absolute value functions.

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Limits at Infinity: Oblique Asymptotes & Horizontal Asymptotes

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  1. AP Calculus AB Day 7 Section 3.5 Perkins

  2. Limits at Infinity NOTE: f(x) may cross horizontal asymptotes near zero. Theorem:

  3. Divide top & bottom by x to the highest power in the denominator. This means the function has an oblique asymptote. To find where, do synthetic division and throw out the remainder. Oblique Asymptote at remainder

  4. ******Because of a radical or an absolute value, we must also check Since x is a negative number, f(x) has horizontal asymptotes at

  5. AP Calculus AB Day 7 Section 3.5 Perkins

  6. Limits at Infinity Theorem:

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