Lesson: Comparing Rate of Growth of Functions Mathematics • Higher Education

In this lesson, we will learn how to use limits to compare the relative magnitudes of functions and their rates of change.

Lesson Plan

Students will be able to

know the formal definition of what it means for one function to dominate another,
understand that the exponential function dominates all polynomial functions.

Q1:

Compare the growth rate of the two functions and using limits as .

Q2:

Consider the functions and .

Evaluate using l’Hôpital’s rule.

What do you get from the two results about the growth rates of and as ?

Q3:

If , what do you notice about the growth rate of compared to as ?