asymptote Synonyms
No Synonyms and anytonyms found
asymptote Meaning
asymptote (n)
a straight line that is the limiting value of a curve; can be considered as tangent at infinity
asymptote (n.)
A line which approaches nearer to some curve than assignable distance, but, though infinitely extended, would never meet it. Asymptotes may be straight lines or curves. A rectilinear asymptote may be conceived as a tangent to the curve at an infinite distance.
asymptote Sentence Examples
- In mathematics, an asymptote is a line that a curve approaches but never intersects.
- The graph of the hyperbola has two asymptotes that the curve gets closer to but never touches.
- As x approaches infinity, the function approaches its horizontal asymptote.
- The vertical line x = 2 is an asymptote of the function y = 1/(x - 2).
- The exponential function has a horizontal asymptote at y = 0 as x approaches negative infinity.
- The oblique asymptote of the rational function y = (2x^2 + 3x - 1) / (x + 2) is y = 2x - 1.
- The curve of the logarithmic function gets closer and closer to the line y = 0 but never intersects it; thus, y = 0 is an asymptote.
- The function y = tan(x) has vertical asymptotes at x = (2n + 1)π/2, where n is an integer.
- The reciprocal function y = 1/x has two asymptotes: the x-axis and the y-axis.
- Understanding the behavior of functions near their asymptotes is crucial in analyzing their properties and graphs.
FAQs About the word asymptote
a straight line that is the limiting value of a curve; can be considered as tangent at infinityA line which approaches nearer to some curve than assignable dist
No synonyms found.
No antonyms found.
In mathematics, an asymptote is a line that a curve approaches but never intersects.
The graph of the hyperbola has two asymptotes that the curve gets closer to but never touches.
As x approaches infinity, the function approaches its horizontal asymptote.
The vertical line x = 2 is an asymptote of the function y = 1/(x - 2).
