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 ...
... are inverse operations if a continuous function is first integrated and then differentiated, the original function is retrieved ... one to compute integrals by using an antiderivative of the function to be integrated ...
... 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 ... 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-axi ... The same volume 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 ...
... 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 ... “calculus book” 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 −1.25 −0.75 ...
More definitions of "function":
- (verb): Serve a purpose, role, or function.
- (noun): A set sequence of steps, part of larger computer program.
Synonyms: routine, subroutine, subprogram, procedure
- (verb): Perform duties attached to a particular office or place or function.
- (noun): What something is used for.
Example: "The function of an auger is to bore holes"
Synonyms: purpose, role, use
- (noun): A vaguely specified social event.
Synonyms: affair, occasion, social occasion, social 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 formal or official social gathering or ceremony.
Example: "It was a black-tie function"
- (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)
“Uses are always much broader than functions, and usually far less contentious. The word function carries overtones of purpose and propriety, of concern with why something was developed rather than with how it has actually been found useful. The function of automobiles is to transport people and objects, but they are used for a variety of other purposesas homes, offices, bedrooms, henhouses, jetties, breakwaters, even offensive weapons.”
—Frank Smith (b. 1928)
“The more books we read, the clearer it becomes that the true function of a writer is to produce a masterpiece and that no other task is of any consequence.”
—Cyril Connolly (19031974)