Day 06 - Continuity and One-sided Limits - 08.24.15

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Bell Ringer

  1. Find if .

    1. 0

    2. undefined

    3. 5

    4. -5

    5. none of the above

  2. Find if .

    1. undefined

    2. -14x

    3. 14x

    4. -14x - 9

    5. none of the above

  3. Find the x-values (if any) at which  is not continuous.

    1. f(x) is continuous for all real x.

    2. f(x) is not continuous at x = 0, –5 and both the discontinuities are nonremovable.

    3. f(x) is not continuous only at x = –5 and f(x) has a removable discontinuity at x = –5 .

    4. f(x) is not continuous only at x = 0 and f(x) has a removable discontinuity at x = 0 .

    5. f(x) is not continuous at x = 0, –5 and f(x) has a removable discontinuity at x = 0 .

  4. Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?

    1. no points of discontinuity.

    2. x = –10 (not removable), x = 3 (removable)

    3. x = –10 (removable), x = 3 (not removable)

    4. no points of continuity.

    5. x = –10 (not removable), x = 3 (not removable)

  5. Find the limit (if it exists).

    1. 1 / 14

    2. 0

    3. 1 / 98

    4. -1 / 14

    5. limits does not exist
Review
  • Math Overview (video)
    • Numbers
    • Relationships
    • Shapes
    • Change
  • Limits
    • Intro to Limits (video)
    • Nonexistent Limits (video)
      • How are limits found numerically and graphically? (checkpoints)
      • How are limits found algebraically? (checkpoints)
Lesson
  • Challenge 3
    • Find a that makes the following function continuous.
    • Find the following limit: 
    • Graph
  • Continuity (video) and One-sided Limits (video)
Exit Ticket
  • Posted on the board at the end of the block
Homework
  • WNQ
  • Last section of Unit 1
Lesson Objectives
  • How can discontinuity of a function be described?
  • How are one-sided limits related to regular limits?

In-Class Help Requests

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