From e021897d1e5a61f6e0e1e690db97a82f3324778b Mon Sep 17 00:00:00 2001 From: arc Date: Thu, 30 Jan 2025 09:23:43 -0700 Subject: [PATCH] vault backup: 2025-01-30 09:23:43 --- .obsidian/plugins/obsidian-git/data.json | 27 ------------------- .../math/MATH1210 (calc 1)/Derivatives.md | 2 ++ 2 files changed, 2 insertions(+), 27 deletions(-) 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)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 6131883..8c7f900 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -55,3 +55,5 @@ $$ f'(x) = \lim_{h \to 0} \dfrac{(x + h)^n - x^n}{h} $$ - Where $n = 3$: $(x + h)^3 = 1x^3h^0 + 3x^2h^1 + 3x^1h^2 + 1x^0h^3 = 1x^3 + 3x^2h + 3xh^2 + 1h^3$ Note that the coefficient follows the associated level of Pascal's Triangle (`1 3 3 1`), and $x$'s power decrements, while $h$'s power increments. The coefficients of each pair will always add up to $n$. Eg, $3 + 0$, $2 + 1$, $1 + 2$, and so on. The **second** term in the polynomial created will have a coefficient of $n$. + +$$ \dfrac{(x + h)^n - x^n}{h} = \lim_{h \to 0} \dfrac{x^n + nx^{n-1}h + p_{n3}x^{n-2}h^2 + \cdots h^n}{} $$ \ No newline at end of file