Lesson: Limits at Infinity Mathematics • Higher Education

In this lesson, we will learn how to evaluate limits of a function when x tends to infinity.

Lesson Plan

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.