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education/math/MATH1210 (calc 1)/Limits.md
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@ -3,7 +3,13 @@ Every mathematical function can be thought of as a set of ordered pairs, or an i
- 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.*** **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 - As an example, given a *well behaved function* $f(x)$ and the fact that:
- $f(1.9) = 8.41$
- $f(1.999) = 8.99401$
- $f(2.1) = 9.61$
- $f(2.01) = 9.061$
- $f(2.0001) = 9.0006$
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$"
# Definitions # Definitions
| Term | Definition | | Term | Definition |