asymptote

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.