Day 07 - Infinite Limits - 08.26.14

Bell Ringer
  • Check Exit Ticket score in PowerSchool
  • Go over previous Exit Ticket
  1. What is the limit from the right of example 1 (posted on board)?

    1. 1

    2. does not exist

    3. infinity

    4. 0

    5. none of the above

  2. What is the limit from the left of example 1 (posted on board)?

    1. 1

    2. does not exist

    3. infinity

    4. 0

    5. none of the above

  3. What is the limit from the right of example 2 (posted on board)?

    1. 1

    2. does not exist

    3. infinity

    4. 0

    5. none of the above

  4. What is the limit from the left of example 2 (posted on board)?

    1. 1

    2. does not exist

    3. infinity

    4. 0

    5. none of the above

Review
  • Finding limits using a table
  • Finding limits using a graph
  • Epsilon-Delta Limit Proofs
  • Limit Properties
    • Dividing Out/Rationalizing Techniques
    • Functions that agree at all but one point
  • One-sided Limits
  • Domains of trig. functions

Lesson
  • Infinite Limits
  • Practice Problems (odds only)
    • page 88 #1-3
    • page 88 #5-7
    • page 88 #13-31
    • page 88 #33-35
    • page 88 #37-53

Exit Ticket
  • Find the limits of the two limit problems posted on the board.
Lesson Objective(s)
  • How can limits be infinite?
  • How are infinite limits explained?

Standard(s)
  • APC.2
    • Define and apply the properties of limits of functions.
      • Limits will be evaluated graphically and algebraically.
        • Includes:
          • ​limits of a constant
          • ​limits of a sum, product, and quotient
          • ​one-sided limits
          • ​limits at infinity, infinite limits, and non-existent limits*
  • APC.3
    • Use limits to define continuity and determine where a function is continuous or discontinuous.
      • Includes:
        • ​continuity in terms of limits
        • continuity at a point and over a closed interval
        • ​application of the Intermediate Value Theorem and the Extreme Value Theorem
        • ​geometric understanding and interpretation of continuity and discontinuity
  • APC.4
    • Investigate asymptotic and unbounded behavior in functions.
      • Includes:
        • describing and understanding asymptotes in terms of graphical behavior and limits involving infinity