Lesson Plan: Existence of Limits Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine whether the limit of a function at a certain value exists.


Students will be able to

  • understand the conditions required for a one-sided limit to exist,
  • understand the conditions required for a limit to exist,
  • understand that equating a limit (or a one-sided limit) to infinity is a certain way of expressing that the limit does not exist,
  • find the limit of a real function in cases where the limit does exist.


Students should already be familiar with

  • one-sided limits,
  • vertical asymptotes,
  • finding limits by direct substitution,
  • finding limits using algebraic techniques, where direct substitution leads to an indeterminate form.


Students will not cover

  • the epsilon–delta definition of a limit,
  • the definition of continuity,
  • the definition of differentiability.

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