Mathematical formulas

Differential Calculus

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Sections

1Notation, functions and domains
2Limits
3Continuity
4Derivative and geometric interpretation
5Differentiation rules
6Higher-order derivatives
7Mean value theorem
8Function analysis
9Optimization
10Linear approximations and differentials
11Taylor series (introduction)
12L'Hôpital and indeterminate limits
13Implicit and related functions
14Related rates
15Graphs and asymptotic behavior
16Guide to differentiate and analyze
AAppendix A: extended derivative table

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Differential Calculus
Limit algebra
Formula

2.4. Limit algebra

Formula

In 2.4. Limit algebra

Formula

\lim_{x\to a}[f(x)]^n=\left[\lim_{x\to a}f(x)\right]^n,\qquad n\in\mathbb{Z},\ \lim_{x\to a}f(x)\neq 0\ \text{if }n<0

Tags

Differential calculus
Limit
Limit algebra

Detail

Valid if the limit of

f

exists. If

n<0

, also requires

\lim_{x\to a}f(x)\neq0

.

Variables

$x$ Independent variable
$a$ Point or real constant
$f$ Function
$n\in\mathbb{Z},\ \lim_{x\to a}f(x)\neq 0\ \text{if }n<0$ Derivative order or exponent

Conditions

$n\in\mathbb{Z},\ \lim_{x\to a}f(x)\neq 0\ \text{if }n<0$

Also known as

power rule for limits
limit of a power

Related topics

Limit algebra

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