Limits
Learn the concept of "limits" and continuity in the context of calculus, and how they can be used to solve real-world problems.
What is Limits?
In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus and mathematical analysis, used to define continuity, derivatives, and integrals.
Formally, a limit is defined as follows: let ƒ be a function defined on some open interval containing a, except possibly at a itself, and let L be a real number. We say that ƒ has a limit L at a, and write
lim_(x→a)ƒ(x)=L
provided that for every ε>0 there exists a δ>0 such that
|ƒ(x)-L|
Limits Resources
Limits Review (Ch 1) - Calculus
I quickly go over my notes for Chapter 1 - Limits. It is a good review for a test or final....
Limits
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”...
Limits
All about limits: the basic idea, finding limits from graphs, different ways to calculate limits, limit laws, one-sided limits, the squeeze theorem, limits at infinity, L'Hospital's rule, and more....