asymptote

(noun)

a straight line which a curve approaches arbitrarily closely, as they go to infinity

Related Terms

  • definition
  • symmetry

Examples of asymptote in the following topics:

  • Horizontal Asymptotes and Limits at Infinity

    • In the first case, $ƒ(x)$ has $y = c$ as asymptote when $x$ tends toward $- \infty$, and in the second that $ƒ(x)$ has $y = c$ as an asymptote as $x$ tends toward $+ \infty$.
    • More general type of asymptotes can be defined as the oblique asymptote case.
    • Only open curves that have some infinite branch, can have an asymptote.
    • No closed curve can have an asymptote.
    • The graph of a function can have two horizontal asymptotes.
  • Infinite Limits

    • If the limit at infinity exists, it represents a horizontal asymptote at $y = L$.
    • Polynomials do not have horizontal asymptotes; such asymptotes may however occur with rational functions.
  • Curve Sketching

    • Determine the asymptotes of the curve.
    • Also determine from which side the curve approaches the asymptotes and where the asymptotes intersect the curve.
  • Improper Integrals

    • An improper Riemann integral of the second kind.The integral may fail to exist because of a vertical asymptote in the function.
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