endpoint

(noun)

Either of the two points at the ends of a line segment.

Related Terms

  • bounded
  • half-bounded interval
  • bounded interval
  • unbounded interval
  • interval
  • open interval
  • closed interval
  • Bounded interval
  • Unbounded interval
  • half-bounded

Examples of endpoint in the following topics:

  • Interval Notation

    • Interval notation uses parentheses and brackets to describe sets of real numbers and their endpoints.
    • The two numbers are called the endpoints of the interval.
    • An open interval does not include its endpoints and is indicated with parentheses.
    • An interval is said to be bounded if both of its endpoints are real numbers.
    • Conversely, if neither endpoint is a real number, the interval is said to be unbounded.
  • Improper Integrals

    • An Improper integral is the limit of a definite integral as an endpoint of the integral interval approaches either a real number or $\infty$ or $-\infty$.
    • An improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or $\infty$ or $-\infty$ or, in some cases, as both endpoints approach limits.
    • in which one takes a limit at one endpoint or the other (or sometimes both).
    • It is often necessary to use improper integrals in order to compute a value for integrals which may not exist in the conventional sense (as a Riemann integral, for instance) because of a singularity in the function, or an infinite endpoint of the domain of integration.
  • Redox Titrations

    • It is therefore possible to see when the titration has reached its endpoint, because the solution will remain slightly purple from the unreacted KMnO4.
    • A student conducts the redox titration and reaches the endpoint after adding 25 mL of the titrant.
    • In this case, starch is used as an indicator; a blue starch-iodine complex is formed in the presence of excess iodine, signaling the endpoint.
    • Note how the endpoint is reached when the solution remains just slightly purple.
  • Fundamental Theorem for Line Integrals

    • Gradient theorem says that a line integral through a gradient field can be evaluated from the field values at the endpoints of the curve.
    • The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.
    • Now suppose the domain $U$ of $\varphi$ contains the differentiable curve $\gamma$ with endpoints $p$ and $q$ (oriented in the direction from $p$ to $q$).
  • The Mean Value Theorem, Rolle's Theorem, and Monotonicity

    • In calculus, the mean value theorem states, roughly: given a planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints .
    • For any function that is continuous on $[a, b]$ and differentiable on $(a, b)$ there exists some $c$ in the interval $(a, b)$ such that the secant joining the endpoints of the interval $[a, b]$ is parallel to the tangent at $c$.
  • Weak Acid-Strong Base Titrations

    • The endpoint and the equivalence point are not exactly the same: the equivalence point is determined by the stoichiometry of the reaction, while the endpoint is just the color change from the indicator.
  • Radiation Reaction

    • We can drop the term from the endpoints if for example the acceleration vanishes at $t=t_1$ and $t=t_2$ or if the acceleration and velocity of the particle are the same at $t=t_1$ and $t=t_2$.We can identify,
  • The Distance Formula and Midpoints of Segments

    • In geometry, the midpoint is the middle point of a line segment, or the middle point of two points on a line, and thus is equidistant from both endpoints.
    • The equation for a midpoint of a line segment with endpoints $(x_{1},y_{1})$and $(x_{2},y_{2})$
  • Line Integrals

    • where $r: [a, b] \to C$ is an arbitrary bijective parametrization of the curve $C$ such that $r(a)$ and $r(b)$ give the endpoints of $C$ and $a$.
    • where $\cdot$ is the dot product and $r: [a, b] \to C$ is a bijective parametrization of the curve $C$ such that $r(a)$ and $r(b)$ give the endpoints of $C$.
  • Estimating a Population Variance

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