Lesson Plan: Limits at Infinity | Nagwa Lesson Plan: Limits at Infinity | Nagwa

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.

Objectives

Students will be able to

  • understand that the limit of 𝑓(𝑥) can take some finite value as 𝑥 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 𝑥 approaches positive or negative infinity is equal to 0,
  • find the limit of a function as 𝑥 approaches 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),
  • unbounded limits.

Exclusions

Students will not cover

  • cases of oscillating behavior,
  • L’Hopital’s rule.

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