# Lesson Plan: Euler’s Number (e) as a Limit Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use the definition of e (Euler’s number) to evaluate some special limits.

#### Objectives

Students will be able to

- recite the function whose infinite limit is Euler’s number,
- recite the function whose limit at zero is Euler’s number,
- evaluate infinite limits or limits at zero resulting in expressions containing Euler’s number by using algebraic manipulation, substitution, and the power rule for limits.
- recite the the function whose limit at zero is the natural logarithm,
- evaluate limits at zero for expressions containing or resulting in the natural logarithm by using algebraic manipulation, substitution, and the power rule for limits.

#### Prerequisites

Students should already be familiar with

- taking infinite limits,
- taking limits at zero,
- substitution in limits,
- the power rule for limits.

#### Exclusions

Students will not cover

- l’Hôpital’s rule for evaluating limits.