diff --git a/.obsidian/plugins/obsidian-git/data.json b/.obsidian/plugins/obsidian-git/data.json index bef4c6e..e69de29 100644 --- a/.obsidian/plugins/obsidian-git/data.json +++ b/.obsidian/plugins/obsidian-git/data.json @@ -1,27 +0,0 @@ -{ - "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 -} \ No newline at end of file diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index bd7eb56..6f2c40f 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -86,11 +86,3 @@ Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ # The Fundamental Theorem of Calculus Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then: $$\int_a^b f(x) dx = F(b) - F(a)$$ -## Proof -## 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 $[a, b]$: -$$ f'(c) = \dfrac{f(b) - f(a)}{x-a} $$ -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. $= \ No newline at end of file