Clever boy club

“If you give a man a crack he’ll be hungry again tomorrow, but if you teach him how to crack, he’ll  never be hungry again”

+ORC

Geometric series:

Consider the series

a + aq + aq^2 + … + aq^n

That series is called geometric serie, with first term a and ratio q (a not equal to 0).

The sum of the first n terms of the geometric serie is (when q not equal 1) :

S_n = (a - aq^n) /(1 - q)

In the study of natural phenomena ans the solution of technical and mathematical problems, one finds it necessary to consider the variation of one quantity as dependent on the variation of another.

For instance, in studies of motion, the path traversed is regarded as a variable wich varies with time. Here, the path traversed is a function of the time.

Let us consider another example. We know that the area of circle, in terms of the radius, is Q = πR^2. If the raduis R takes on a variety of numerical value, the area Q will also assume various numerical values. Thus, the variation of one variable brings about a variation in the other. Here, the area of a circle Q is a function of the radius R. Let us formulate a definition of the concept function:

Function definition : If to each value of the variable x (within a certain range) there corresponds one definite value of another variable y, then y is a function of x or, in function notation, y=f(x), y=β(x), and so forth.

The variable x is called the independent variable or argument. The relation between the variables x and y is called a functional relation. The letter f in the functional notation y=f(x) indicates that some kind of operations must be performed on the value of x in order to obtain the value of y.

The notation y=C, where C is a constant, denotes a function whose value for anyvalue of x is the same and is equal to C.

Function definition (domain): The set of values of x for which the values of the function y are determined by virtue of the rule f(x) is called domain of definition of the function.

Esta tabla de primitivas contiene las primitivas más abituales de 28 funciones.

Tabla de primitivas

Algunas pequeñas demostraciones, con sutiles errores que permiten llegar a resultados como las igualdades 1=2 o 1=-1, demostrando algunas trampas que proponen las matemáticas.

Falsas demostraciones