Limits at infinity - exponential functions
- Grades
- High School
- Pages
- 13
- File type
- Microsoft PowerPoint
- Answer key
- Included
- Subject
- Math, Algebra, Calculus
- Topic
- Limits at infinity, Exponential functions
- Resource types
- Lesson Plans, Presentations
- Answer key
- Included
Product description
From the author
PowerPoint presentation, 13 slides explaining how to calculate the limit of exponential functions, as the function approaches either to positive or negative infinity.
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In the classroom
Teaching tips & learning objectives
Learning objectives
Understand the concept of limits at infinity and horizontal asymptotes for exponential functions
Teaching tips
This deck explicitly builds on a prior lesson on limits at infinity of polynomials (slide 2); review that factoring-the-dominant-term technique before this lesson so students recognize it being reapplied to exponential expressions.
Walk through the sign of the exponent's own limit first (slides 5-6) before moving to the multi-term factoring examples (slides 9-12), since later problems depend on correctly reading whether the exponent itself goes to positive or negative infinity.
Skills covered
Evaluating basic exponential limits at infinity — recognizing that e^x -> infinity as x -> infinity and e^x -> 0 as x -> -infinity
Applying the limit-of-a-product property when the exponent of an exponential term is itself a polynomial limit
Factoring out the dominant exponential term in a multi-term expression to evaluate a limit at infinity
Good to know
Questions teachers ask about this resource
How does this lesson connect to limits of polynomials?
It explicitly reuses the polynomial-limits technique of factoring out the dominant term, applying the same idea to exponential expressions by factoring out an appropriate dominant exponential term for the direction of the limit, using the denominator’s growth when working with fractions.
What kinds of limit problems are worked through?
The slides progress from simple direct-evaluation limits of e^x, to limits where the exponent is itself a polynomial limit, to more involved rational expressions with exponential terms in both the numerator and denominator.
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Resource details
Concepts & topics
Core concepts
Core concepts
Limits at infinity
Exponential functions
Horizontal asymptotes
Topics
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