vault backup: 2025-03-06 09:54:22

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

@@ -0,0 +1,27 @@
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+  "showStatusBar": true,
+  "updateSubmodules": false,
+  "syncMethod": "merge",
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+  "treeStructure": false,
+  "refreshSourceControl": true,
+  "basePath": "",
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education/math/MATH1210 (calc 1)/Limits.md

@@ -99,3 +99,12 @@ To evaluate an indeterminate product ($0 * \infty$), use algebra to convert the
 $$ \lim_{x \to 0^+} x\ln(x) = \lim_{x \to 0^+}\dfrac{\ln x}{\dfrac{1}{x}} = \lim_{x \to 0^+} \dfrac{1/x}{-1/(x^2)} = \lim_{x \to 0^+} -x = 0 $$
 # Indeterminate form $(\infty - \infty)$:
 If the $\lim_{x \to a}f(x) = \infty$  and $\lim_{x \to a} (g(x)) = \infty$ , then $\lim_{x \to a}(f(x) - g(x))$ may or may not exist.
+
+# Indeterminate Powers
+When considering the $\lim_{x \to a} f(x)^{g(x)}$, the following are indeterminate:
+- $0^0$
+- $\infty^0$
+- $1^\infty$ 
+
+1. $lim_{x \to 0^+} x
+