22 lines
1.1 KiB
Markdown
22 lines
1.1 KiB
Markdown
# Introduction
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Every mathematical function can be thought of as a set of ordered pairs, or an input value and an output value.
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- Examples include $f(x) = x^2 + 2x + 1$, and $\{(1, 3), (2, 5), (4, 7)\}$.
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**A limit describes how a function behaves *near* a point, rather than *at* that point.***
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- As an example, given a *well behaved function* $f(x)$ and the fact that:
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- $f(1.9) = 8.41$
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- $f(1.999) = 8.99401$
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- $f(2.1) = 9.61$
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- $f(2.01) = 9.061$
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- $f(2.0001) = 9.0006$
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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$"
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# Definitions
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| Term | Definition |
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| --------------------- | ----------------------------------------------------------------------------- |
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| Well behaved function | A function that is continuous, has a single value, and is defined everywhere. |
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