vault backup: 2025-03-06 09:39:22

.obsidian/plugins/obsidian-git/data.json

@@ -1,27 +0,0 @@
-{
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-  "autoCommitMessage": "vault backup: {{date}}",
-  "commitDateFormat": "YYYY-MM-DD HH:mm:ss",
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-  "autoPullInterval": 5,
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-  "pullBeforePush": true,
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-  "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
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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 $\lim_{x \to a}(f(x) * g(x)$ 
+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.
+
+$$ \lim_{x \to 0^+} x\ln(x) = \lim_{x \to 0^+}\dfrac{\ln x}{\dfrac{1}{x}} = \\lim_{x \to 0^+} \dfrac{1/x}{-1/(x^2)} = \lim_{x \to 0^+} -x = 0 $$