- Math in the Real World Discussion
- Grades based on tests
- Challenging yourself
- Asking questions in class
Bell Ringer
Find if . 0 undefined 5 -5 none of the above
Find if . undefined -14x 14x -14x - 9 none of the above
Find the x-values (if any) at which is not continuous. f(x) is continuous for all real x. f(x) is not continuous at x = 0, –5 and both the discontinuities are nonremovable. f(x) is not continuous only at x = –5 and f(x) has a removable discontinuity at x = –5 . f(x) is not continuous only at x = 0 and f(x) has a removable discontinuity at x = 0 . f(x) is not continuous at x = 0, –5 and f(x) has a removable discontinuity at x = 0 .
Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable? no points of discontinuity. x = –10 (not removable), x = 3 (removable) x = –10 (removable), x = 3 (not removable) no points of continuity. x = –10 (not removable), x = 3 (not removable)
Find the limit (if it exists).  1 / 14 0 1 / 98 -1 / 14 - 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?
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
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