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  2. Continuous function - Wikipedia

    en.wikipedia.org/wiki/Continuous_function

    the sinc-function becomes a continuous function on all real numbers. The term removable singularity is used in such cases when (re)defining values of a function to coincide with the appropriate limits make a function continuous at specific points. A more involved construction of continuous functions is the function composition.

  3. Uniform continuity - Wikipedia

    en.wikipedia.org/wiki/Uniform_continuity

    Linear functions + are the simplest examples of uniformly continuous functions. Any continuous function on the interval [ 0 , 1 ] {\displaystyle [0,1]} is also uniformly continuous, since [ 0 , 1 ] {\displaystyle [0,1]} is a compact set.

  4. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise. Minkowski's question mark function: Derivatives vanish on the rationals. Weierstrass function: is an example of continuous function that is nowhere differentiable

  5. These Calculators Make Quick Work of Standard Math ... - AOL

    www.aol.com/best-calculators-students...

    With more than 120 different built-in functions, such as amortization, cash flow, and loan payments, this HP financial calculator makes quick work of your accounting—whether it’s personal or ...

  6. Bisection method - Wikipedia

    en.wikipedia.org/wiki/Bisection_method

    The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps: Calculate c, the midpoint of the interval, c = ⁠ a + b / 2 ⁠.

  7. Lipschitz continuity - Wikipedia

    en.wikipedia.org/wiki/Lipschitz_continuity

    A function is called locally Lipschitz continuous if for every x in X there exists a neighborhood U of x such that f restricted to U is Lipschitz continuous. Equivalently, if X is a locally compact metric space, then f is locally Lipschitz if and only if it is Lipschitz continuous on every compact subset of X .

  8. Piecewise function - Wikipedia

    en.wikipedia.org/wiki/Piecewise_function

    its sub-functions are continuous on the corresponding intervals (subdomains), there is no discontinuity at an endpoint of any subdomain within that interval. The pictured function, for example, is piecewise-continuous throughout its subdomains, but is not continuous on the entire domain, as it contains a jump discontinuity at . The filled ...

  9. Intermediate value theorem - Wikipedia

    en.wikipedia.org/wiki/Intermediate_value_theorem

    Intermediate value theorem: Let be a continuous function defined on [,] and let be a number with () < < ().Then there exists some between and such that () =.. In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between () and () at some point within the interval.