From 236165cdd221e429c0a40f64a0a5ddda6e2eb1a6 Mon Sep 17 00:00:00 2001 From: arc Date: Tue, 7 Jan 2025 18:29:44 -0700 Subject: [PATCH] vault backup: 2025-01-07 18:29:44 --- education/math/MATH1210 (calc 1)/Limits.md | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Limits.md b/education/math/MATH1210 (calc 1)/Limits.md index 811bd50..c5dd15c 100644 --- a/education/math/MATH1210 (calc 1)/Limits.md +++ b/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 |