From 51bfc78a36f6dd8a4281cacf8213dd6e470c2bea Mon Sep 17 00:00:00 2001 From: arc Date: Tue, 21 Jan 2025 12:49:38 -0700 Subject: [PATCH] vault backup: 2025-01-21 12:49:38 --- education/math/MATH1210 (calc 1)/Limits.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/education/math/MATH1210 (calc 1)/Limits.md b/education/math/MATH1210 (calc 1)/Limits.md index a45d17b..ab0171a 100644 --- a/education/math/MATH1210 (calc 1)/Limits.md +++ b/education/math/MATH1210 (calc 1)/Limits.md @@ -27,6 +27,8 @@ To find this limit if it exists we must perform some mathematical manipulations # Limits of the Form $\frac{k}{0}, k \ne 0$ If we have a one sided limit of the form $\lim_{x \to a^*} \frac{f(x)}{g(x)}$ $f(x) \to k (k \ne 0)$ and $g(x) \to 0$ as $x \to a$ then: $$ \lim_{x \to a^*} \frac{f(x)}{g(x)} = \infty \space or \space \lim_{x \to a^*} \frac{f(x)}{g(x)} = -\infty $$ +# Limits of the Form $\frac{\infty}{\infty}$ +If we have a limit of the form $\lim_{x \to a} \frac{f(x)}{g(x)}$ where both $f(x) \to \infty$ and $g(x) \to \infty$ as $x \to a$ then the limit may or may not exist and is said to be an indeterminate form of type $\frac{\infty}{\infty}$ # Continuity A function is continuous if their graph can be traced with a pencil without lifting the pencil from the page.