From 20650f291617bd9bb39842b5c892bc4b96cd01e6 Mon Sep 17 00:00:00 2001 From: arc Date: Tue, 21 Jan 2025 13:00:48 -0700 Subject: [PATCH] vault backup: 2025-01-21 13:00:48 --- education/math/MATH1210 (calc 1)/Limits.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Limits.md b/education/math/MATH1210 (calc 1)/Limits.md index 35ac4b1..400f4c0 100644 --- a/education/math/MATH1210 (calc 1)/Limits.md +++ b/education/math/MATH1210 (calc 1)/Limits.md @@ -30,7 +30,9 @@ $$ \lim_{x \to a^*} \frac{f(x)}{g(x)} = \infty \space or \space \lim_{x \to a^*} # 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 $\frac{\infty}{\infty}$. -To find the limit if it exists we must perform some algebraic manipulations on the quotient in +To find the limit if it exists we must perform some algebraic manipulations on the quotient in order to change the form of the function. + +If $f(x)$ and $g(x)$ are polynomials, then we can multiply the numerator and denominator by $\dfrac{1}{x^n}$, where $n$ is the degree of the polynomial in the denominator. # Continuity A function is continuous if their graph can be traced with a pencil without lifting the pencil from the page.