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education/math/MATH1210 (calc 1)/Limits.md
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# Introduction # Introduction
- Every mathematical function can be thought of as a set of ordered pairs, or an input value and an output value. Every mathematical function can be thought of as a set of ordered pairs, or an input value and an output value.
- Examples include $f(x) = x^2 + 2x + 1$, and $\{(1, 3), (2, 5), (4, 7)\}$. - Examples include $f(x) = x^2 + 2x + 1$, and $\{(1, 3), (2, 5), (4, 7)\}$.
**A limit describes how a function behaves *near* a point, rather than *at* that point.***
- As an example, given a well behaved function~ $f(x)$ and $f(2) = 9$, we can assume that
# Definitions # Definitions
| Term | Definition | | Term | Definition |
| --------------------- | ----------------------------------------------------------------------------- |
| Well behaved function | A function that is continuous, has a single value, and is defined everywhere. |
| | |