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In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over the interval (a,b) is defined by: [1] ¯ = ().
On the other hand, if a function's domain is continuous, a table can give the values of the function at specific values of the domain. If an intermediate value is needed, interpolation can be used to estimate the value of the function. For example, a portion of a table for the sine function might be given as follows, with values rounded to 6 ...
Law of the unconscious statistician: The expected value of a measurable function of , (), given that has a probability density function (), is given by the inner product of and : [34] [()] = (). This formula also holds in multidimensional case, when g {\displaystyle g} is a function of several random variables, and f {\displaystyle f} is ...
The value of the function at a maximum point is called the maximum value of the function, denoted (()), and the value of the function at a minimum point is called the minimum value of the function, (denoted (()) for clarity). Symbolically, this can be written as follows:
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
The value of a function, given the value(s) assigned to its argument(s), is the quantity assumed by the function for these argument values. [1] [2] For example, if the function f is defined by f (x) = 2 x 2 – 3 x + 1, then assigning the value 3 to its argument x yields the function value 10, since f (3) = 2·3 2 – 3·3 + 1 = 10.
More precisely, if : is a real-valued function (or, more generally, a function taking values in some additive group), its zero set is (), the inverse image of {} in . Under the same hypothesis on the codomain of the function, a level set of a function f {\displaystyle f} is the zero set of the function f − c {\displaystyle f-c} for some c ...
A function that takes a single argument as input, such as () =, is called a unary function. A function of two or more variables is considered to have a domain consisting of ordered pairs or tuples of argument values. The argument of a circular function is an angle. The argument of a hyperbolic function is a hyperbolic angle.