Limits at infinity - exponential functions

A 13-slide calculus deck walks through evaluating limits at infinity for exponential functions, from basic e^x behaviour through seven fully worked limit problems using the factor-out-the-dominant-term technique.

Year groups: Years 11–13
File type: Microsoft PowerPoint
Use: Digital activity

Updated Sep 18, 2021

Subject: Maths
Topic: Limits, Calculus
Resource types: Lesson Plans, Teacher Tools
Use: Digital activity

From the author

About this resource

PowerPoint presentation, 13 slides explaining how to calculate the limit of exponential functions, as the function approaches either to positive or negative infinity.

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
Evaluating limits of rational expressions with exponential terms in both the numerator and denominator

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 the exponential term with the largest (or most negative) exponent before dividing through.

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

Limits at infinity
Exponential functions
Horizontal asymptotes

Topics

Limits Calculus Exponential Limits Limits With Exponential Functions Limit of an Exponential

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Categories this resource belongs to

Maths Lesson Plans Teacher Tools Year 13 Year 12 Year 11

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