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 ...
... 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 ... 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 ... can be obtained via 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 surface and the plane.) If the number ...
... and integration are inverse operations if a continuous function is first integrated and then differentiated, the original function is retrieved ... allows one to compute integrals by using an antiderivative of the function to be integrated ...
... Some integrals cannot be found exactly, some require special functions which themselves are a challenge to compute, and others are so complex that finding the exact answer is too slow ... approach 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 ...
More definitions of "function":
- (noun): A vaguely specified social event.
Synonyms: affair, occasion, social occasion, social function
- (verb): Perform duties attached to a particular office or place or function.
- (verb): Serve a purpose, role, or 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 relation such that one thing is dependent on another.
Example: "Height is a function of age"; "price is a function of supply and demand"
- (noun): A mathematical relation such that each element of one set is associated with at least one element of another set.
Synonyms: mathematical function
- (noun): What something is used for.
Example: "The function of an auger is to bore holes"
Synonyms: purpose, role, use
- (noun): A formal or official social gathering or ceremony.
Example: "It was a black-tie function"
Famous quotes containing the word function:
“The fact remains that the human being in early childhood learns to consider one or the other aspect of bodily function as evil, shameful, or unsafe. There is not a culture which does not use a combination of these devils to develop, by way of counterpoint, its own style of faith, pride, certainty, and initiative.”
—Erik H. Erikson (19041994)
“The function of literature, through all its mutations, has been to make us aware of the particularity of selves, and the high authority of the self in its quarrel with its society and its culture. Literature is in that sense subversive.”
—Lionel Trilling (19051975)
“The art of living is to function in society without doing violence to ones own needs or to the needs of others. The art of mothering is to teach the art of living to children.”
—Elaine Heffner (20th century)