Preview of the calculus topic of limits

Limits basics

Limits are the core tool that we build upon for calculus. Many times, a function can be undefined at a point, but we can think about what the function "approaches" as it gets closer and closer to that point (this is the "limit"). Other times, the function may be defined at a point, but it may approach a different limit. There are many, many times where the function value is the same as the limit at a point. Either way, this is a powerful tool as we start thinking about slope of a tangent line to a curve. If you have a decent background in algebra (graphing and functions in particular), you'll hopefully enjoy this tutorial!
Intro to limits
What are limits?
Limits intuition
Introduction to the intuition behind limits

Finding limits algebraically

We often attempt to find the limit at a point where the function itself is not defined. In this tutorial, we will use algebra to "simplify" functions into ones where it is defined. Given that the original function and the simplified one may be identical except for the limit point in question, this is a useful way of finding limits.
Finding limits algebraically
In this example we find the limit of a function near an undefined point by simplifying the function near that point.
Limit properties
What is the limit of the sum of two functions?  What about the product?
Two-sided limits using algebra
Practice finding two-sided limits by simplifying functions algebraically.
Two-sided limits using advanced algebra
Watch Sal find a tricky limit by factoring a cubic expression.
Two-sided limits using advanced algebra
Practice finding two-sided limits using advanced algebra