# Limit (mathematics)/Limits

Limits of Functions

## Basics

edit### What are limits?

editLimits are a way to calculate the value that a function approaches. For instance, we could calculate the value of the function f(x) as x approaches 2. Just as easily we can calculate the value of f(x) as x approaches 20, -2, π, 0, or even ∞.

### Why would anyone need limits?

editThere are a number of reasons that someone might want to use limits:

- 1. To find the values of functions with asymptotes or missing points
- 2. To calculate the slope of a point in calculus
- 3. To prove derivatives in calculus

## Notation

editThe notation of a limit function is fairly simple:

This says limit (lim) of f(x) as x approaches p is L.

Usually f(x) is substituted with the contents of the function like so:

## Properties

edit

## Sample Problem Set #1

editLet's say we have the function . If we want to find the limit as x approaches 4, then:

Using two properties of limits:

and

Our problem becomes:

If we think about the graph of y=b, then we know that the y value never changes. Which means that at any point on that line, we can expect y to be equal to b. So, for any number b:

For us, this means that: