From cfda79dc6a87990174b9b5a6ea0980e6a1384458 Mon Sep 17 00:00:00 2001
From: arc <zleyyij@users.noreply.github.com>
Date: Thu, 6 Mar 2025 09:39:22 -0700
Subject: [PATCH] vault backup: 2025-03-06 09:39:22
---
.obsidian/plugins/obsidian-git/data.json | 27 ----------------------
education/math/MATH1210 (calc 1)/Limits.md | 6 ++++-
2 files changed, 5 insertions(+), 28 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)/Limits.md b/education/math/MATH1210 (calc 1)/Limits.md
index 124c5c9..25d6caf 100644
--- a/education/math/MATH1210 (calc 1)/Limits.md
+++ b/education/math/MATH1210 (calc 1)/Limits.md
@@ -92,4 +92,8 @@ L'Hospital's rule **cannot** be used in any other circumstance.
2. $= \lim_{x \ to 0}\dfrac{7^x \ln(7) -5^x(\ln(5)}{2}$
3. $= \dfrac{\ln(7) - \ln(5)}{2}$
# Indeterminate form $(0 * \infty)$
-If the $\lim_{x \to a}f(x) = 0$ and $\lim_{x\to a} g(x) = \infty$ then $\lim_{x \to a}(f(x) * g(x)$
\ No newline at end of file
+If the $\lim_{x \to a}f(x) = 0$ and $\lim_{x\to a} g(x) = \infty$ then $\lim_{x \to a}(f(x) * g(x)$ may or may not exist.
+
+To evaluate an indeterminate product ($0 * \infty$), use algebra to convert the product to an equivalent quotient and then use L'Hopsital's Rule.
+
+$$ \lim_{x \to 0^+} x\ln(x) = \lim_{x \to 0^+}\dfrac{\ln x}{\dfrac{1}{x}} = \\lim_{x \to 0^+} \dfrac{1/x}{-1/(x^2)} = \lim_{x \to 0^+} -x = 0 $$
\ No newline at end of file