Lesson Plans
Algebra 1
8 units
Geometry
10 units
Algebra 2
9 units
Precalculus
11 units
AP Precalculus
8 units
AP Calculus
9 units
Unit 1: Intro to Calculus
18 days
Day 1: Introducing Calculus: Can Change Occur at an Instant?
Day 2: Defining Limits and Using Limit Notation
Day 3: Estimating Limits from Graphs
Day 4: Using Algebraic Approaches to Evaluate Limits
Day 5: Selecting Procedures for Evaluating Limits & Quiz Review
Day 6: Quiz 1.1 to 1.7
Day 7: Introduction to Squeeze Theorem
Day 8: Connecting Multiple Representations
Day 9: Continuity and Discontinuity
Day 10: Removing Discontinuities
Day 11: Review Topics 1.8-1.13
Day 12: Quiz 1.8 to 1.13
Day 13: Limits Involving Infinity
Day 14: Intermediate Value Theorem
Day 15: Intermediate Value Theorem
Day 16: Unit 1 Review Day 1
Day 17: Unit 1 Review Day 2
Day 18: Unit 1 Test
Unit 2: Differentiation
18 days
Unit 3: Differentiating Composite, Implicit, and Inverse Functions
11 days
Unit 4: Contextual Applications of Differentiation
14 days
Unit 5: Analytical Applications of Derivatives
13 days
Unit 6: Integration and Accumulation of Change
21 days
Unit 7: Differential Equations
11 days
Unit 8: Applications of Integration
17 days
Unit 9: Selected BC Lessons
10 days
Intro Stats
11 units
AP Statistics
13 units
Day 13: Limits Involving Infinity
Limits Involving Infinity (Topics 1.14-1.15)
Learning Targets

Understand that evaluating a limit at infinity is the same thing as finding the end behavior/horizontal asymptote.

Use the rules for end behavior of rational functions to determine a limit at infinity.

Describe vertical asymptotes and unbounded behavior using infinite limits.

Tasks/Activity
Time
Activity
20 minutes
Debrief Activity with Margin Notes
15 minutes
QuickNotes
10 minutes
Check Your Understanding
10 minutes
Activity: How Much Do We Remember From School?
Lesson Handouts
Answer Key
Experience First

This lesson connects students’ prior knowledge about horizontal asymptotes and end behavior with the new concept and notation of finding limits as x approaches infinity. They study a function that models memory over time and compare graphical and analytical representations of this function’s long-run behavior. Emphasis is placed on interpreting situations in context and connecting concepts.

Formalize Later

This lesson focuses on rational functions and the end-behavior of two polynomials at x-values near infinity. If presented with a quotient containing other functions (transcendentals), end behavior can often be determined by comparing the dominance of the numerator or denominator using the mnemonic Ten Fabulous Engineers Prefer Learning Calculus. Tower functions (x^x^x) grow faster than Factorials (x!) grow faster than Exponentials (a^x) grow faster than Polynomials (x^n) grow faster than Logarithms grow faster than Constants. Students will learn other methods for evaluating limits for complex functions, but memorizing TFEPLC can guide their reasoning at this stage.

Exam Insights

Limits at infinity have appeared on both the multiple choice and free response sections of the exam. Check out this great question! (1998 AB 2a).

Student Misconceptions

Horizontal asymptotes describe the behavior of a function at the ends of the number line. A function may attain this value or cross this horizontal line many times before asymptotic behavior appears.