Course: Calculus I
Topic: Limits and Continuity
Subtopic: Limits Graphically


The first big topic in calculus is limits. As x gets closer and closer to a number, f(x) gets closer and closer (approaches) a value. This is the concept of a limit. The answer from the limit is the value that f(x) is approaching.

In this lesson we analyze limits graphically. We'll observe the graph of f(x) and see what value the outputs are approaching as the input x gets closer and closer to a given number in an intuitive manner.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: limit, approach (in terms of a limit), D.N.E. = does not exist, one-sided limit

Text Notes

Mini-Lectures and Examples

STUDY: Limits - Graphically and Numerically

Supplemental Resources (recommended)

Watch What is Calculus?, Michael Harrison (Socratica) and What is Calculus Used For?, Jeff Heys, TEDx Talk.

Supplemental Resources (optional)

Watch What is Calculus? by James Sousa (MathIsPower4U) or read Why Do We Study Calculus? by Prof. Eric Schechter of Vanderbilt University.

Video: Calculating Limits Intuitively, Selwyn Hollis's Video Calculus

Geogebra Exploration: Intuitive Notion of the Limit, Mark Renault

Lesson: Slopes and Velocities, Dale Hoffman's Contemporary Calculus overviews several applications of calculus for motivational purposes. You are NOT expected to know solve these problems ... yet!

Video Examples: MathIsPower4U | Calculus I is an excellent resource of short tutorial video examples particularly in instances when you need an additional example of a specific type of problem. This week watching any of the videos listed under "Limits" category may be helpful

rev. 2020-10-10