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education/math/MATH1210 (calc 1)/Limits.md

@@ -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 $\{(1, 3), (2, 5), (4, 7)\}$.
 
 **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
 
 | Term                  | Definition                                                                    |