Day 09 - Limits Problems - 08.28.14

Bell Ringer
  • Create a problem involving one of the concepts covered in chapter 1. Include an answer key with multiple ways to solve the problem.
    • Evaluating Limits Algebraically
    • Evaluating Limits Graphically
    • Evaluating Limits Numerically
    • Removable Discontinuity
    • Nonremovable Discontinuity
    • One-sided Limits
    • Infinite Limits
  • Stump Your Teacher Problems

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
  • Infinite Limits

Lesson

  1. Find the values of the constants a and b such that



  1. Consider the function

    1. Find the domain of f.

    2. Calculate

    3. Calculate


  1. Determine all value of the constant a such that the following function is continuous for all real numbers.


Exit Ticket

  1. The function f and its graph are shown below:

    1. Calculate the limit of f(x) as x gets closer to 2 from the left side.

    2. Which value is greater?

      1. the limit of f(x) as x goes to 1

      2. f(1)

      3. Explain your answer.

    3. At what value(s) of c on the interval [0, 4] does the limit of f(x) as x goes to c not exist?

      1. Explain your answer.

Lesson Objective(s)
  • How are the concepts in chapter 1 related?

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