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vault backup: 2025-03-27 09:51:27

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arc 2025-03-27 09:51:27 -06:00
parent d78c1ecd7a
commit 6776d3e417
2 changed files with 31 additions and 2 deletions
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27
.obsidian/plugins/obsidian-git/data.json vendored
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@ -0,0 +1,27 @@
{
"commitMessage": "vault backup: {{date}}",
"autoCommitMessage": "vault backup: {{date}}",
"commitDateFormat": "YYYY-MM-DD HH:mm:ss",
"autoSaveInterval": 5,
"autoPushInterval": 0,
"autoPullInterval": 5,
"autoPullOnBoot": true,
"disablePush": false,
"pullBeforePush": true,
"disablePopups": false,
"listChangedFilesInMessageBody": false,
"showStatusBar": true,
"updateSubmodules": false,
"syncMethod": "merge",
"customMessageOnAutoBackup": false,
"autoBackupAfterFileChange": false,
"treeStructure": false,
"refreshSourceControl": true,
"basePath": "",
"differentIntervalCommitAndPush": false,
"changedFilesInStatusBar": false,
"showedMobileNotice": true,
"refreshSourceControlTimer": 7000,
"showBranchStatusBar": true,
"setLastSaveToLastCommit": false
}

4
education/math/MATH1210 (calc 1)/Integrals.md
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@ -87,8 +87,10 @@ Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$
Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then: Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then:
$$\int_a^b f(x) dx = F(b) - F(a)$$ $$\int_a^b f(x) dx = F(b) - F(a)$$
## Proof ## Proof
## Mean Value Theorem ## Mean Value Theorem
Between the interval $[a, b]$, the average rate of change of a function **must be equal** to at least one point between $[a, b]$: Between the interval $[a, b]$, the average rate of change of a function **must be equal** to at least one point between $[a, b]$:
$$ f'(c) = \dfrac{f(b) - f(a)}{x-a} $$ $$ f'(c) = \dfrac{f(b) - f(a)}{x-a} $$
For some $c$ between $a$ and $b$. For some $c$ between $a$ and $b$.
1. $F(b) - F(a) = F(x_1) - F(x_0)$
2. $= (F(x_1) - F(x_0) + (F(x_2) - F(x_1) + (F(X_3) - F(X_2) + \cdots + (F(x_n) - f(x_{n - 1})$ 3. $=