Lesson Plan: Limits at Infinity Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to evaluate limits of a function when 𝑥 tends to infinity.
Students will be able to
- understand that the limit of can take some finite value as approaches positive or negative infinity,
- conceptually relate limits at infinity to horizontal asymptotes,
- understand that the laws of limits still apply for limits at positive or negative infinity,
- understand how to manipulate and evaluate limits using the fact that the limit of a reciprocal function as approaches positive or negative infinity is equal to 0,
- find the limit of a function as approaches positive or negative infinity.
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),
- unbounded limits.
Students will not cover
- cases of oscillating behavior,
- L’Hopital’s rule.