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Understanding Infinite Limits and Graph Asymptotes

Explore vertical asymptotes, behavior around x=0, and infinite limits in this detailed guide. Learn to evaluate limits at infinity for rational functions efficiently. Find examples and explanations in this comprehensive resource.

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Understanding Infinite Limits and Graph Asymptotes

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  1. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Does not exist number number

  2. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Consider the function: Study the behavior of the function around x=0. Vertical Asymptote

  3. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Vertical Asymptote

  4. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  5. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  6. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  7. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Infinite Limits

  8. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  9. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Vertical Asymptote&

  10. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Find all vertical asymptotes

  11. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs EXAMPLE

  12. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Does not exist number number

  13. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Example:

  14. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  15. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Example: Example: Example:

  16. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Limits at Infinity of Rational Functions To evaluate the limit at infinity of any rational function, we first divide both the numerator and denominator by the highest power of that occurs in the denominator. Example:

  17. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Example: Remark: To evaluate the limit at infinity of any rational function, we first divide both the numerator and denominator by the highest power of that occurs in the denominator. Example: Remark:

  18. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Notes: Notes:

  19. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Notes: Notes:

  20. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Example: Example: (ex80p116) Multiply by conjugate radical.

  21. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  22. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Example: Example:

  23. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Vertical Asymptote& Horizontal Asymptote& The line Is a horizontal asymptote

  24. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: The line Is a horizontal asymptote

  25. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: The line Is a horizontal asymptote

  26. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example:

  27. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs EXAM-1 TERM-121

  28. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Sec 2.2

  29. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs To evaluate the limit at infinity of any rational function, we first divide both the numerator and denominator by the highest power of that occurs in the denominator. Multiply by conjugate radical. Factor then take the limit

  30. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Oblique Asymptote Vertical Asymptote Horizontal Asymptote If the degree of the numerator of a rational function is 1 greater than the degree of the denominator, the graph has an oblique or slant line asymptote. We find an equation for the asymptote by dividing numerator by denominator Remark:

  31. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Who is going faster to infinity Example:

  32. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Example: Sketch the graph of

  33. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  34. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Exam1-Term101

  35. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs a b

  36. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Limit Laws

  37. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  38. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  39. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs

  40. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Do you have the graph Find From the graph study the limit from right and left Does f contain greatest integer or absolute value Study the limit from right and left Substitute and find the limit Can we use Direct substitution Use: 1)factor then cancel 2)Multiply by conjugate 3)Make common denominator Write f as: Use squeeze theorem

  41. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Sandwich thm Factor then take the limit high pwr in denomi Rational func Containing radicals Containing absolute value Remove the | | Containing noninteger Multiply by conjugate radical. Use Use graph Use

  42. Sec 2.6:Limits Involving Infinity; Asymptotes of Graphs Reminder: After sec2.5 continuity

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