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.

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