vault backup: 2025-03-06 09:44:22
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.obsidian/plugins/obsidian-git/data.json
vendored
27
.obsidian/plugins/obsidian-git/data.json
vendored
@ -0,0 +1,27 @@
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{
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"commitMessage": "vault backup: {{date}}",
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"autoCommitMessage": "vault backup: {{date}}",
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"commitDateFormat": "YYYY-MM-DD HH:mm:ss",
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"autoSaveInterval": 5,
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"autoPushInterval": 0,
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"autoPullInterval": 5,
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"autoPullOnBoot": true,
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"disablePush": false,
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"pullBeforePush": true,
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"disablePopups": false,
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"listChangedFilesInMessageBody": false,
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"showStatusBar": true,
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"updateSubmodules": false,
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"syncMethod": "merge",
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"customMessageOnAutoBackup": false,
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"autoBackupAfterFileChange": false,
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"treeStructure": false,
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"refreshSourceControl": true,
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"basePath": "",
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"differentIntervalCommitAndPush": false,
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"changedFilesInStatusBar": false,
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"showedMobileNotice": true,
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"refreshSourceControlTimer": 7000,
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"showBranchStatusBar": true,
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"setLastSaveToLastCommit": false
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}
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@ -88,7 +88,7 @@ The above problem can be solved more easily *without* L'Hospital's rule, the lea
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L'Hospital's rule **cannot** be used in any other circumstance.
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## Examples
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1. $\lim_{x \ to 0} \dfrac{7^x - 5^x}{2x}$
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1. $\lim_{x \to 0} \dfrac{7^x - 5^x}{2x}$
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2. $= \lim_{x \ to 0}\dfrac{7^x \ln(7) -5^x(\ln(5)}{2}$
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3. $= \dfrac{\ln(7) - \ln(5)}{2}$
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# Indeterminate form $(0 * \infty)$
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@ -96,4 +96,4 @@ If the $\lim_{x \to a}f(x) = 0$ and $\lim_{x\to a} g(x) = \infty$ then $\lim_{x
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To evaluate an indeterminate product ($0 * \infty$), use algebra to convert the product to an equivalent quotient and then use L'Hopsital's Rule.
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$$ \lim_{x \to 0^+} x\ln(x) = \lim_{x \to 0^+}\dfrac{\ln x}{\dfrac{1}{x}} = \\lim_{x \to 0^+} \dfrac{1/x}{-1/(x^2)} = \lim_{x \to 0^+} -x = 0 $$
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$$ \lim_{x \to 0^+} x\ln(x) = \lim_{x \to 0^+}\dfrac{\ln x}{\dfrac{1}{x}} = \lim_{x \to 0^+} \dfrac{1/x}{-1/(x^2)} = \lim_{x \to 0^+} -x = 0 $$
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