calculus

            
             A function, in mathematics, is used to indicate the relationship between two or more quantities. For example, the term function can be used to designate a power xn of a variable x. In addition, it can be applied to various geometric aspects of a curve, such as its slope. The concept of a function is also related to the Dirichlet concept. Dirichlet regarded y = x2 - 3x + 5 as a function which is thought of as the rule that determines y for a given x of an ordered pair of the function; thus, the preceding rule determines (3, 5), (-4, 33) as two of the infinite number of elements of the function. A function as a variable y, called the dependent variable, having its values fixed or determined in some definite manner by the values assigned to the independent variable x, or to several independent variables x1, x2,", xk. The values of both the dependent and independent variables were real or complex numbers. The statement y = f (x), read "y is a function of x," indicated the dependence between the variables x and y; f (x) is given as a specific formula, such as f (x) = x2 - 3x + 5, or by a rule stated in words, such as f (x) is the first integer larger than x for all x's that are real numbers. Graphically, there exists even functions where f (-x)= f (x) for all x domain (f) and odd functions where f (-x) = -f (x) for all x domain (f) and is symmetric about the origin. Through the usage of the vertical line test, a curve on a plane is the graph of a function if the line does not intersect the curve in more than one point.
             The fundamental concept of calculus, is the limit and is the source from which all its theory and applications are developed, is the theory of limits of functions of variables, which symbolize an arbitrary element in a given set (usually the set of real numbers). Let f be a function of the real variable x, which is denoted f (x), defined on some set of real numbers containing the number x0.