https://math.stackexchange.com › questions › 4280473 › explanation-for-the-shortcut-trick-to...

$$\lim _{x\rightarrow \infty }\dfrac{N}{D}=\dfrac{a}{b} $$, where $a$ and $b$ are the coefficient of the highest power in the numerator and the coefficient of highest power in the denominator respectively.

https://math.stackexchange.com › ... › when-to-use-lhospitals-rule-vs-the-limit-shortcut

Consider the limit $\lim \limits_{x \to \infty}\frac{3x^2+14x-5}{x^2+x-12}$. It can quickly be determined that the $x$ approaches $3$ using L'Hospital's rule. The same answer can be derived, however, by using this shortcut (I am unaware if it has a specific name):

https://math.libretexts.org › Courses › Hartnell_College › MATH_25:_PreCalculus_(Abramson...

Finding the Limit of a Sum, a Difference, and a Product. Graphing a function or exploring a table of values to determine a limit can be cumbersome and time-consuming. When possible, it is more efficient to use the properties of limits, which is a collection of theorems for finding limits.

https://www.symbolab.com › cheat-sheets › Limits

Limit Chain Rule. \mathrm {if}\:\lim_ {u\:\to\:b}\:f (u)=L,\:\mathrm {and}\:\lim_ {x\:\to\:a}g (x)=b,\:\mathrm {and}\:f (x)\:\mathrm {is\:continuous\:at}\:x=b. \mathrm {Then:}\:\lim_ {x\:\to\:a}\:f (g (x))=L. Math Cheat Sheet for Limits.

https://www.nagwa.com › fr › explainers › 376145415074

Définition : Limite d’une fonction. Si les valeurs de 𝑓 (𝑥) s’approchent d’une valeur 𝐿 quand les valeurs de 𝑥 s’approchent de 𝑎 (des deux côtés) mais pas nécessairement quand 𝑥 = 𝑎, alors on dit que la limite de 𝑓 (𝑥) quand 𝑥 tend vers 𝑎 est égale à 𝐿 et on la note l i m → 𝑓 (𝑥) = 𝐿.

https://openstax.org › books › calculus-volume-1 › pages › 4-6-limits-at-infinity-and-asymptotes

In this section, we define limits at infinity and show how these limits affect the graph of a function. At the end of this section, we outline a strategy for graphing an arbitrary function f. f. Limits at Infinity. We begin by examining what it means for a function to have a finite limit at infinity.

https://tutorial.math.lamar.edu › pdf › Calculus_Cheat_Sheet_All.pdf

Limits. Definitions. Precise Definition : We say lim f(x) = L if for. x!a. every " > 0 there is a > 0 such that whenever. Limit at Infinity : We say lim f(x) = L if we can. x!1. make f(x) as close to L as we want by taking x. 0 < jx. aj < then jf(x) Lj < ". large enough and positive. “Working” Definition : We say lim f(x) = L if. x!a.