Limit (mathematics)/Limits
Limits of Functions
Basics
[edit | edit source]What are limits?
[edit | edit source]Limits 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?
[edit | edit source]There 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
[edit | edit source]The 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
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Sample Problem Set #1
[edit | edit source]Let'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: