infinity

Examples of infinity in the following topics:

• Infinite Limits

  • Limits involving infinity can be formally defined using a slight variation of the $(\varepsilon, \delta)$-definition.
  • Limits involving infinity can be formally defined using a slight variation of the $(\varepsilon, \delta)$-definition.
  • If the degree of $p$ is greater than the degree of $q$, then the limit is positive or negative infinity depending on the signs of the leading coefficients;
  • If the limit at infinity exists, it represents a horizontal asymptote at $y = L$.
  • Therefore, the limit of this function at infinity exists.

• Precise Definition of a Limit

  • Therefore, the limit of this function at infinity exists.
  • Therefore, the limit of this function at infinity exists.

• Finding Limits Algebraically

  • The limit of $f(x)= \frac{-1}{(x+4)} + 4$ as $x$ goes to infinity can be segmented down into two parts: the limit of $\frac{−1}{(x+4)}$ and the limit of $4$.
  • Therefore, the limit of $f(x)$ as $x$ goes to infinity is $4$.

• Cylinders and Quadric Surfaces

  • A cylinder can be seen as a polyhedral limiting case of an $n$-gonal prism where $n$ approaches infinity.

• Curve Sketching

  • Similarly, removing all but the terms of highest order from the equation and solving gives the points where the curve meets the line at infinity.

• Indeterminate Forms and L'Hôpital's Rule

  • That limit could converge to any number, or diverge to infinity, or might not exist, depending on what the functions $f$ and $g$ are.

• Sequences

  • The infinity symbol, $\infty$, is often used as the superscript to represent the sequence that includes all integer $k$-values starting with a certain one.

• Improper Integrals

  • Such an integral is often written symbolically just like a standard definite integral, perhaps with infinity as a limit of integration.