Some articles on function, functions:
... 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 ... 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 ...
... 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 ...
... 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 ...
... cannot be found exactly, some require special functions which themselves are a challenge to compute, and others are so complex that finding the exact ... 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 −1.7 ...
... are inverse operations if a continuous function is first integrated and then differentiated, the original function is retrieved ... theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated ...
More definitions of "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): 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"
- (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"
- (verb): Perform duties attached to a particular office or place or function.
- (verb): Serve a purpose, role, or 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:
“Literature does not exist in a vacuum. Writers as such have a definite social function exactly proportional to their ability as writers. This is their main use.”
—Ezra Pound (18851972)
“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)
“Any translation which intends to perform a transmitting function cannot transmit anything but informationhence, something inessential. This is the hallmark of bad translations.”
—Walter Benjamin (18921940)