Some articles on function, functions:
... 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 ...
... 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 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 ... 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 region between the surface ...
... 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 answer is too slow ... 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 ...
More definitions of "function":
- (noun): What something is used for.
Example: "The function of an auger is to bore holes"
Synonyms: purpose, role, use
- (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 mathematical relation such that each element of one set is associated with at least one element of another set.
Synonyms: mathematical function
- (noun): A vaguely specified social event.
Synonyms: affair, occasion, social occasion, social function
- (verb): Serve a purpose, role, or function.
- (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.
Famous quotes containing the word function:
“Think of the tools in a tool-box: there is a hammer, pliers, a saw, a screwdriver, a rule, a glue-pot, nails and screws.The function of words are as diverse as the functions of these objects.”
—Ludwig Wittgenstein (18891951)
“Every boy was supposed to come into the world equipped with a father whose prime function was to be our father and show us how to be men. He can escape us, but we can never escape him. Present or absent, dead or alive, real or imagined, our father is the main man in our masculinity.”
—Frank Pittman (20th century)
“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)