From 232b5f2709704bc62d2ce6ee27da5425be190c29 Mon Sep 17 00:00:00 2001 From: arc Date: Sun, 26 Jan 2025 17:57:19 -0700 Subject: [PATCH] vault backup: 2025-01-26 17:57:19 --- education/math/MATH1210 (calc 1)/Derivatives.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 6a6c09c..2f9cc9a 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -11,7 +11,9 @@ As the distance between the two points $a$ and $b$ grow smaller, we get closer a If we have the coordinate pair $(a, f(a))$, and the value $h$ is the distance between $a$ and another $x$ value, the coordinates of that point can be described as ($(a + h, f(a + h))$. With this info: - The slope of the secant line can be described as $\dfrac{f(a + h) - f(a)}{a + h - a}$, which simplifies to $\dfrac{f(a + h) - f(a)}{h}$. -- The slope of the *tangent line* or the *instantaneous velocity* can be found by taking the limit of the above function as the distance ($h$) approaches zero: $\lim_{h \to 0}\dfrac{f(a + h) - f(a)}{h}$ +- The slope of the *tangent line* or the *instantaneous velocity* can be found by taking the limit of the above function as the distance ($h$) approaches zero: +$$\lim_{h \to 0}\dfrac{f(a + h) - f(a)}{h}$$ +The above formula can be used to find the *derivative*. This may also be referred to as the *instantaneous velocity*, or the *instantaneous rate of change*. # Line Types ## Secant Line A **Secant Line** connects two points on a graph.