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The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.
RExcel is an add-on for Microsoft Excel that allows access to the statistics package R from within Excel. It uses the statconnDCOM server and, for certain configurations, the room package. It uses the statconnDCOM server and, for certain configurations, the room package.
The scope of the function name is limited to the let expression structure. In mathematics, the let expression defines a condition, which is a constraint on the expression. The syntax may also support the declaration of existentially quantified variables local to the let expression. The terminology, syntax and semantics vary from language to ...
Holomorphic functions of several complex variables satisfy an identity theorem, as in one variable : two holomorphic functions defined on the same connected open set and which coincide on an open subset N of D, are equal on the whole open set D. This result can be proven from the fact that holomorphics functions have power series extensions ...
Multivalued functions of a complex variable have branch points. For example, for the nth root and logarithm functions, 0 is a branch point; for the arctangent function, the imaginary units i and −i are branch points. Using the branch points, these functions may be redefined to be single-valued functions, by restricting the range.
x m,i (also called independent variables, explanatory variables, predictor variables, features, or attributes), and a binary outcome variable Y i (also known as a dependent variable, response variable, output variable, or class), i.e. it can assume only the two possible values 0 (often meaning "no" or "failure") or 1 (often meaning "yes" or ...
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables (multivariate), rather than just one. [1]
An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. [ 1 ] : 204–206 For example, the equation x 2 + y 2 − 1 = 0 {\displaystyle x^{2}+y^{2}-1=0} of the unit circle defines y as an implicit function ...