Some articles on function, functions:
... Let f be a continuous real-valued function defined on a closed interval ... Let F be the function defined, for all x in, by Then, F is continuous on, differentiable on the open interval (a, b), and for all x in (a, b) ... Let f be a real-valued function defined on a closed interval that admits an antiderivative g on ...
... For instance, a sequence of functions can frequently be constructed that approximate, in a suitable sense, the solution to a problem ... Then the integral of the solution function should be the limit of the integrals of the approximations ... However, many functions that can be obtained as limits are not Riemann integrable, and so such limit theorems do not hold with the Riemann integral ...
... cannot be found exactly, some require special functions which themselves are a challenge to compute, and others are so complex that finding the exact ... divides the integration range into, say, 16 equal pieces, and computes function values ... Spaced function values x −2.00 −1.50 −1.00 −0.50 0.00 0.50 1.00 1.50 2.00 f(x) 2.22800 2.45663 2.67200 2.32475 0.64400 −0.92575 −0.94000 −0.16963 0.83600 x −1.75 −1.25 −0.75 ...
... In general, an integral over a set E of a function f is written Here x need not be a real number, but can be another suitable quantity, for instance, a vector in R3 ... Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables ... the triple integral — the integral of a function in three variables — of the constant function f(x, y, z) = 1 over the above mentioned region between the ...
... the statement that differentiation and integration are inverse operations if a continuous function is first integrated and then differentiated, the original function is ... allows one to compute integrals by using an antiderivative of the function to be integrated ...
More definitions of "function":
- (noun): A formal or official social gathering or ceremony.
Example: "It was a black-tie function"
- (noun): The actions and activities assigned to or required or expected of a person or group.
Example: "The function of a teacher"
Synonyms: office, part, role
- (noun): A set sequence of steps, part of larger computer program.
Synonyms: routine, subroutine, subprogram, procedure
- (noun): A vaguely specified social event.
Synonyms: affair, occasion, social occasion, social function
- (noun): What something is used for.
Example: "The function of an auger is to bore holes"
Synonyms: purpose, role, use
- (verb): Serve a purpose, role, or function.
Synonyms: serve
- (verb): Perform duties attached to a particular office or place or function.
Synonyms: officiate
- (noun): A mathematical relation such that each element of one set is associated with at least one element of another set.
Synonyms: mathematical function
Famous quotes containing the word function:
“The press and politicians. A delicate relationship. Too close, and danger ensues. Too far apart and democracy itself cannot function without the essential exchange of information. Creative leaks, a discreet lunch, interchange in the Lobby, the art of the unattributable telephone call, late at night.”
—Howard Brenton (b. 1942)
“The mother’s and father’s attitudes toward the child correspond to the child’s own needs.... Mother has the function of making him secure in life, father has the function of teaching him, guiding him to cope with those problems with which the particular society the child has been born into confronts him.”
—Erich Fromm (1900–1980)
“The uses of travel are occasional, and short; but the best fruit it finds, when it finds it, is conversation; and this is a main function of life.”
—Ralph Waldo Emerson (1803–1882)