Mathematical formulas

Differential Calculus

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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
Oblique asymptotes
Formula

15.3. Oblique asymptotes

Formula

In 15.3. Oblique asymptotes

Formula

\text{For }x\to+\infty:\ m_+=\lim_{x\to+\infty}\frac{f(x)}{x},\ b_+=\lim_{x\to+\infty}[f(x)-m_+x];\quad \text{for }x\to-\infty:\ m_-=\lim_{x\to-\infty}\frac{f(x)}{x},\ b_-=\lim_{x\to-\infty}[f(x)-m_-x]

Tags

Differential calculus
Derivative
Graph
Oblique asymptotes

Detail

Slope and intercept for oblique asymptotes (apply separately at

+\infty

and

-\infty

).

Variables

$x$ Independent variable
$b$ Interval endpoint or constant
$f$ Function

Conditions

$\text{for }x\to-\infty:\ m_-=\lim_{x\to-\infty}\frac{f(x)}{x},\ b_-=\lim_{x\to-\infty}[f(x)-m_-x]$

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Related formulas

Related
Formula
$y=mx+b\text{ is an oblique asymptote} \Leftrightarrow \lim_{x\to+\infty}[f(x)-(mx+b)]=0\ \text{or}\ \lim_{x\to-\infty}[f(x)-(mx+b)]=0$
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