Day 06 - One-sided Limits - 08.25.14

Bell Ringer

  • Finding limits using a table
  • Finding limits using a graph
  • Epsilon-Delta Limit Proofs
  • Finding Limit Properties
    • Dividing Out/Rationalizing Techniques
  • Give an example of two functions that agree at all but one point.
  • Limit Properties

  • One-sided Limits
    • page 78 #1-5 (odds)
    • page 79 #7-21 (odds)
    • page 79 #35-51 (odds)

Exit Ticket
  • Find the limit of the following function analytically.
    • Note: Function will be written on the board in class.
  • Create a function that has neither removable or nonremovable discontinuity.
Lesson Objective(s)
  • How are one-sided limits related to two-sided limits?
  • How are the types of continuity similar and different?

  • 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