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education/math/MATH1210 (calc 1)/Limits.md
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@ -9,13 +9,19 @@ Every mathematical function can be thought of as a set of ordered pairs, or an i
- $f(2.1) = 9.61$
- $f(2.01) = 9.061$
- $f(2.0001) = 9.0006$
We can note that the smaller the distance of the input value $x$ to $2$, the smaller the distance of the output to $9$. This is most commonly described in the terms "As $x$ approaches $2$, $f(x)$ approaches $9$. $ \rarrow$"
We can note that the smaller the distance of the input value $x$ to $2$, the smaller the distance of the output to $9$. This is most commonly described in the terms "As $x$ approaches $2$, $f(x)$ approaches $9$", or "As $x \to 2$, $f(x) \to 9$."
Limits are valuable because they can be used to describe a point on a graph, even if that point is not present.
# Standard Notation
The standard notation for a limit is:
$$ \lim_{x \to a} f(x) = L $$
- As $x$ approaches $a$, the output of $f(x)$ draws closer to $L$.
# Definitions
| Term | Definition |
| --------------------- | ----------------------------------------------------------------------------- |
| Well behaved function | A function that is continuous, has a single value, and is defined everywhere. |
| | |