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What are the ways in which the limit of functions are determined?
How is continuity determined?
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Student Learning Map
- Topic:Limits and Continuity
- Subject(s):Math
- Days:25
- Grade(s):11, 12
Key Learning:
Determine the limit of given functions and whether the function is continuous.
Unit Essential Question(s):
Concept: Rates of Change and Limits Concept: Continuity and Tangent Lines Lesson Essential Question(s):How is the one-sided limit of a function determined? (A)How are general limits of functions determined? (A)Why do some limits fail to exist? (A)Why do some limits fail to exist? (ET)Lesson Essential Question(s):How do you calcuate the limit as "x approaches infinity" and what does it indicate? (A)How do you calcuate the limit as "x approaches infinity" and what does it indicate? (ET)How can the limit approach infinity when x is approaching a finite number? (A)How can the limit approach infinity when x is approaching a finite number? (ET)Lesson Essential Question(s):What are three conditions for continuity at a point? (A)What is the meaning of the Intermediate Value Theorem for Continuous Functions? (A)What is the meaning of the Intermediate Value Theorem for Continuous Functions? (ET)What are types of discontinuity? (A)How is the equation of a tangent line to a curve written? (A)
Additional Info:
Calculus textbook Graphing Calculator Powerpoint from the Internet (G.Kelly) TI-Presenter Ancillary material
Resources:
Culminating Activities:
1. Untitled Culminating ActivityStudent Assessment(s):
1. Untitled Student AssessmentAcquisition Lesson(s):
1. How is the one-sided limit of a function determined?2. How do you calcuate the limit as "x approaches infinity" and what does it indicate?3. What are three conditions for continuity at a point?4. How are general limits of functions determined?5. Why do some limits fail to exist?6. How can the limit approach infinity when x is approaching a finite number?7. What is the meaning of the Intermediate Value Theorem for Continuous Functions?8. What are types of discontinuity?9. How is the equation of a tangent line to a curve written?Extended Thinking Lesson(s):
1. How do you calcuate the limit as "x approaches infinity" and what does it indicate?2. Why do some limits fail to exist?3. How can the limit approach infinity when x is approaching a finite number?4. What is the meaning of the Intermediate Value Theorem for Continuous Functions?