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

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arc 2025-03-06 09:54:22 -07:00
parent 2fb3e9cea0
commit e3db5505f7
2 changed files with 37 additions and 1 deletions

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@ -0,0 +1,27 @@
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@ -98,4 +98,13 @@ 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.
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