Math Study Notes

Classification of functions Algebraic functions In algebraic functions, the operations to be carried out with the independent variable are: Addition , Subtraction , Multiplication , Division , Empowerment and Radication . The algebraic functions include: Explicit functions If the images of x can be obtained by simple substitution. f (x) = 5x – 2. Implicit functions If the images of x cannot be obtained by simple substitution, it is … Read more

Pascal’s triangle . Also called the Tartaglia Triangle for having proposed a rectangular scheme of the binomial coefficients, Nicola Tartaglia . Long before the previous ones it is known as the Yan Hui triangle (1303) in China, and in Iran as the Jayyam triangle (1100). And in Europe, as an arithmetic triangleit is a triangular arrangement of rows increasing in number of elements that are positive integers, from … Read more

Limit of a function at a point. Given a function f defined in a reduced neighborhood V of the point x 0 , f is said to have a limit L, when x tends towards x 0 , if whatever is the sequence {x 0 } of points in the neighborhood V that converges towards x 0 , the sequence of the images {f (x n )} converges towards L. Informally, the fact that … Read more

Infinitesimo. An infinitesimal, infinitely small quantity, used in infinitesimal calculus , are defined as limits and considered as numbers in practice. Summary [ hide ] 1 Definition 1 Examples 2 Properties 3 infinitesimal comparables 4 infinitely many equivalents 5 Definition of order of an infinitesimal 6 Sources Definition A function y = f (x) is infinitely small, infinitesimal or infinitesimal when x → a (or when x → ∞) if and … Read more

Infinito . If for any number N, as large as you want, that there exists such δ (N), for 0 <Ι x – a Ι <δ (N) the inequality Ιf (x) Ι> N is verified, the function f (x ) is called infinite (infinitely large) when x → a. Similarly, f (x) is determined as infinite (infinitely large) … Read more

Transformation of formulas (Calculation of predicates) . In “propositional normal forms” the equivalence relation establishes, for each formula, an equivalence class. Within each of these classes, there is a set of members (formulas) that have a particular structure that makes them the object of special interest. These are the normal ways. Obviously, if the relationship “logical equivalence” is also present in the Calculation … Read more