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  2. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...

  3. Limit (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Limit_(mathematics)

    In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

  4. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    Although implicit in the development of calculus of the 17th and 18th centuries, the modern idea of the limit of a function goes back to Bolzano who, in 1817, introduced the basics of the epsilon-delta technique (see (ε, δ)-definition of limit below) to define continuous functions.

  5. Video shows arrest of Olympian Fred Kerley after ...

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    At 11:22 p.m., Miami Beach officers were involved in an investigation on the 100 block of Ninth Street. According to the arrest report: "Officers subsequently were approached by a black Male ...

  6. L'Hôpital's rule - Wikipedia

    en.wikipedia.org/wiki/L'Hôpital's_rule

    L'Hôpital's rule (/ ˌ l oʊ p iː ˈ t ɑː l /, loh-pee-TAHL) or L'Hospital's rule, also known as Bernoulli's rule, is a mathematical theorem that allows evaluating limits of indeterminate forms using derivatives.

  7. James Dean Told Elizabeth Taylor His Childhood Priest ...

    www.aol.com/lifestyle/james-dean-told-elizabeth...

    Richard C. Miller/Donaldson Collection/Getty. Elizabeth Taylor and James Dean on the set of 'Giant' in 1955.

  8. Mortgage and refinance rates for Dec. 26, 2024: Rates for 30 ...

    www.aol.com/finance/mortgage-and-refinance-rates...

    See today's average mortgage rates for a 30-year fixed mortgage, 15-year fixed, jumbo loans, refinance rates and more — including up-to-date rate news.

  9. Characterizations of the exponential function - Wikipedia

    en.wikipedia.org/wiki/Characterizations_of_the...

    Then = + +! + +! (again, one must use lim inf because it is not known if t n converges). Now, take the above inequality, let m approach infinity, and put it together with the other inequality to obtain: lim sup n → ∞ t n ≤ e x ≤ lim inf n → ∞ t n {\displaystyle \limsup _{n\to \infty }t_{n}\leq e^{x}\leq \liminf _{n\to \infty }t_{n ...