What is a Limit?

[nycmathguy]

According to mathisfun.com, the word limit is all about APPROACHNG.

Here is what the site has posted as a definition:

"Sometimes we can't work something out directly but we can see what it should be as we get closer and closer!"

Well, what on earth does that mean?
Before sharing the math definition of a limit, how do you define a limit in Calculus?

Limits is how we do calculus. So, it's important, right?

You say?

 

[MathLover1]

In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity.

as you can see above, as x approaches 2 (but never equals 2) from the left (also from the right) the value of y approaches 4

Limits Definition
Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as

It is read as “the limit of f of x, as x approaches c equals L”. The “lim” shows limit, and fact that function f(x) approaches the limit L as x approaches c is described by the right arrow.

 

[nycmathguy]

In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity.

as you can see above, as x approaches 2 (but never equals 2) from the left (also from the right) the value of y approaches 4

Limits Definition
Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as

View attachment 2414
It is read as “the limit of f of x, as x approaches c equals L”. The “lim” shows limit, and fact that function f(x) approaches the limit L as x approaches c is described by the right arrow.

I think calculus will be a very interesting road to travel.