WordNet-Online
Free dictionary and thesaurus of English. Definitions, synonyms, antonyms and more...
Hint: double-click any word to get it searched!

	Enter your search terms Submit search form
	Web www.wordnet-online.com

Definitions from WordNet

Definitions from the Web

Asymptote

Definition:

An asymptote is a straight line that a curve approaches but never touches.

Senses:

1. Mathematics

1. A line that a curve approaches but never reaches, as it heads towards infinity or a specific point.
2. A line that a function gets arbitrarily close to, but never quite reaches, as it tends towards infinity or zero.

Examples:

Mathematics:

1. The graph of the function y = 1/x has a vertical asymptote at x = 0.

2. As the value of x approaches infinity, the curve of the function y = e^x gets arbitrarily close to the horizontal asymptote y = 0.

Sample Sentences:

1. The graph of the equation y = 1/x has two asymptotes, a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

2. The function y = tan(x) has vertical asymptotes at odd multiples of π/2.

3. In calculus, understanding the behavior of functions near their asymptotes is essential for analyzing their limits and derivatives.

Related Products:

Explore related books on asymptotes:

• Books on Asymptotes in Calculus
• Books on Asymptotes in Mathematics