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Warm-Up: September 20, 2012

Warm-Up: September 20, 2012. Identify all asymptotes of the graph of. Homework Questions?. Limits Involving Infinity. Section 2.2. Limits Involving Infinity. Horizontal Asymptotes. The line y=b is a horizontal asymptote if or. Example 1. Vertical Asymptotes.

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Warm-Up: September 20, 2012

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  1. Warm-Up: September 20, 2012 • Identify all asymptotes of the graph of

  2. Homework Questions?

  3. Limits Involving Infinity Section 2.2

  4. Limits Involving Infinity

  5. Horizontal Asymptotes • The line y=b is a horizontal asymptote if or

  6. Example 1

  7. Vertical Asymptotes • The line x=a is a vertical asymptote if or

  8. Example 2 • Find the vertical asymptotes of the graph of f(x) • Describe the behavior of f(x) to the left and right of each vertical asymptote

  9. Properties of Limits as x±∞ • Same as when xc (yesterday’s notes) • Sandwich Theorem can still be used

  10. Example 3

  11. Assignment • Read Section 2.2 (pages 65-71) • Page 71 Exercises #1-27 odd

  12. Warm-Up: September 21, 2012 • Determine the end behavior of the graphs of the following functions

  13. Homework Questions?

  14. End Behavior Models • Graph the following on the same window with [-3, 3] by [-10, 10] • New window: [-30, 30] by [-10000, 100000] • New window: [-300, 300] by [-10000, 108]

  15. End Behavior Model • The function g is a right end behavior model for fiff • The function g is a left end behavior model for fiff

  16. Example 4 • Find a power function end behavior model for the given function and identify any horizontal asymptotes

  17. Example 5 • Find a simple basic function as a right end behavior model and as a left end behavior model.

  18. Example 6 • Use the graph of y=f(1/x) to find:

  19. Quiz Time! • Clear everything off of your desk except a pencil and eraser. • If you have passed both quizzes, begin working on: • Page 72 #29-32 all, 33-47 odd

  20. Classwork • Complete #4 on the back of the Limits Worksheet

  21. Assignment • Read Section 2.2 (pages 65-71) • Page 72 #29-32 all, 33-47 odd

  22. September 24, 2012 • Pick up a Limits Worksheet and start working

  23. Homework Questions?

  24. Limits Graphs Worksheet • 1) a) 4 a) 1 • b) 4 b) 1 • c) 4 c) 1 • 2) a) 1 a) -1 • b) 2 b) -1 • c) DNE c) -1 • 3) a) -∞ a) DNE • b) ∞ b) 0 • c) DNE c) DNE

  25. Classwork • Complete #4 on the back of the Limits Graphs Worksheet

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