Lesson Plan: Unbounded Limits
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to investigate limits that tend to infinity as 𝑥 approaches a finite value.
Objectives
Students will be able to
- understand that the limit of can be said to “equal” positive or negative infinity as approaches some finite value,
- understand that the one-sided limits of may not be “equal” to each other in
cases of unbounded limits:
- one of the one-sided limits may be “equal” to positive or negative infinity,
- both of the one-sided limits may be “equal” to infinity (and they may agree on the sign, positive or negative),
- both of the one-sided limits may be “equal” to infinity (and they may disagree on the sign, positive and negative),
- understand that equating a limit to positive or negative infinity is a particular way of expressing that the limit does not exists, but it still provides useful information,
- conceptually relate unbounded limits to vertical asymptotes,
- find values of that cause the limit of the function to “equal” positive or negative infinity.
Prerequisites
Students should already be familiar with
- horizontal and vertical asymptotes,
- one-sided and normal limits,
- laws of limits,
- finding limits by direct substitution,
- finding limits using algebraic techniques (where direct substitution leads to an indeterminate form).
Exclusions
Students will not cover
- cases of oscillating behavior,
- L’Hôpital’s rule,
- oblique asymptotes,
- limits at infinity.