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The Lame Joke of the day.. What do cats eat for breakfast? And now it’s time for.. Mice Krispies!
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Limits & infinity (horizontal & vertical asymptotes) AP Calc

Dec 05, 2014

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Ron Eick

Limits & infinity (horizontal & vertical asymptotes) AP Calc
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  • 1. The Lame Joke of the day.. What do cats eat for breakfast? And now its time for.. Mice Krispies!
  • 2. Vertical Asymptotes Vertical asymptotes occur when a function is undefined (usually the zeros of the denom.) At a vertical asymptotes, the limit of the function is +/- infinity ( does not exist) At the asymptote, the function increases or decreases without bound. Also, )(lim)(lim xfxf cxcx
  • 3. 2 vertical asymptotes
  • 4. Practice Find the vertical asymptotes of each function: 1 1 )( x xf 3 )2( 4 )( x xf 16 2 )( 4 2 t tt xf
  • 5. Vertical Asymptotes - exceptions The exception is when you can cancel common factors - YOU get a hole instead of an asymptote
  • 6. Limits at infinity How do you find the limit of a function when x approaches +/- infinity? YOU FIND THE HORIZONTAL ASYMPTOTES Tells you the end behavior of the graph.)(lim xf x
  • 7. How do we find the horizontal asymptotes? Compare the degrees of the numerator and denominator. Degrees equal: Its the ratio of the leading coefficients. Degree of numerator is greatest: No asymptote. The function is unbounded at the ends. (Goes on forever to infinity) Degree of denominator is greatest: y = 0 (x-axis) is horizontal asymptote
  • 8. Example 1 12 lim x x x
  • 9. Example 13 52 lim 2 x x x
  • 10. Example 13 52 lim 2 3 x x x
  • 11. Practice Evaluate each limit xx 1 lim 13 23 lim 2 x x x 13 25 lim 4 4 x xx x
  • 12. AP Calculus Warm up