# 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.