The Uniform Continuity of Functions on Normed Linear Spaces
... are points of S, and Y is a subset of S. Let us consider X, S, T and let us consider f . We say that f is uniformly continuous on X if and only if the conditions (Def. 1) are satisfied. (Def. 1)(i) X ⊆ dom f, and (ii) for every r such that 0 < r there exists s such that 0 < s and for all x1 , x2 suc ...
... are points of S, and Y is a subset of S. Let us consider X, S, T and let us consider f . We say that f is uniformly continuous on X if and only if the conditions (Def. 1) are satisfied. (Def. 1)(i) X ⊆ dom f, and (ii) for every r such that 0 < r there exists s such that 0 < s and for all x1 , x2 suc ...
Exam 1 - FAU Math
... 3. (a) What is a one-to-one function? How can you tell that a function is one-to-one by looking at its graph? Solution. A one-to-one function is one that assigns different values to different points in the domain. precisely: A function f of domain D is one-to-one if (and only if) f (s) 6= f (t) when ...
... 3. (a) What is a one-to-one function? How can you tell that a function is one-to-one by looking at its graph? Solution. A one-to-one function is one that assigns different values to different points in the domain. precisely: A function f of domain D is one-to-one if (and only if) f (s) 6= f (t) when ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.