Matemathics III

Pia de matematicas

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Universidad Autónoma de Nuevo León Resultado de imagen para universidad autonoma de nuevo leon Resultado de imagen para preparatoria 1

PIA

MATEMATHICS III

Name: José Luis Aguirre Galarza

Teacher: Sergio Bustamante

Roll Number: 1

ID: 1864016

Group: 301

Introduction

In this semester we learned different things along this same, it was very important that in order to solve the problems that were given to us in the stages we had to pay attention in class, since these topics are of great importance if you want to study an engineering or some architecture, but in spite of that, we all had to attend to the indications

Also they come to help us in chemistry, to want to calculate the pH of some substances we must use the logarithmic functions. Mathematics are too helpful to increase our agility solving problems, finding solutions, etc. Many people said or think that mathematics are useless but it´s a great instrument that is used in many works.

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Glossary

* In an equation is called independent variable that is assigned freely values, while variable whose values depend on it is called dependent variable.

* Domain: The domain of a function or relation is the set of all values of the independent variable.

* Range: The range of a function is the set of values of a dependent variable corresponding to all values of an independent variable in the domain.

* Relation: Is any set of ordered pairs of any correspondence between sets.

* Function: is a especial class of relation for which there is exactly one value of the dependent variable (y) and for each value of the independent variable (x) in the domain.

* Asymptote: An asymptote is a line that the graph of a function approaches zero; in the other words, the distance between the cure and the line approaches zero. For the cases that we will study in this course, the line will touch the asymptote.

* Linear function: Is a function which general equation is y= mx + b, where m and b are constants and m ≠ 0.

* Slope m: The slope m of a linear function is the radio run/rise, where run is the horizontal distance between two points of the graph and rise is the vertical distance between them (note that rise and run can be positive or negative).

* Intercepts of a graph: Y-intercept of a function is the value of y, when x=0. The x-intercept of a function is the value of x, when y=0.

* Inequality: It is called inequality to any expression that refers to the relation between two numbers and therefore has the symbol “>” or “<”. It is called inequation to the inequality which has an unknown quantity.

* The general quadratic equation is: y = ax2 + bx + c

* Let a, b, and c be constants, can have any value, except a ≠ 0 (a = 0, it would be a line equation).

* i is the imaginary unit

* i is a number squared produce -1

* i2 = -1 therefore, i = √-1

* Complex number: A complex number is the sum of the real and an imaginary number, and has the form a + bi, “a” and “b” are real numbers and “i” is imaginary unit.

* Complex conjugate number: The complex conjugates a + bi, that differ only in the sign of the imaginary part, are called complex conjugates, to each other.

* Factor Theorem: x – b is factor of P (x), if and only if P (x) = 0

* Rational root theorem: a x – b is a factor of P (x) if and only is P (b/a) = 0 d

* A number “r” is a root or a solution of a function if P (x) = 0.

* Algebraic rational function: An algebraic rational function (or simply rational function) is a function whose general equation is f (x) = P (x)/ Q (x)

* Where P (x) and Q (x) are polynomials, Q (x) ≠0.

* Algebraic irrational function: is one that appears inside a radical. (Instead of a radical it could be fractional exponent).

* If “k” and “n” are constants, then “y varies directly with the nth power of x”, this means that: y = K x n

* While if “y variables inversely with the nth power of x”, this means that y = k/xn

* “multiplication – multiplication” property of variation functions: If y = Kxn, then, when we multiplying the “x” value by the “c” constant multiplies the function, “y” value by the “c” constant.

* If y = K/xn then when we multiplying the “x” value by the “c” constant, the function divides the value of “y” by the “c” constant.

* Exponential function: Is a function in which its general equation is y = a. bx, where a and b represent constants, b is positive, and x, y are the independent and dependent variables respectively.

* Powers: For positive integer exponent xn means that the product of n times and x as a factor.

* Negative exponents: For the expression x-n it is defined as: 1/xn*

* For exponent zero x0 = 1, if always x ≠ 0.

* Cubic root: The “nth root” is a number that when it is raised to a nth power its answer is “x”. It Is represented by the radical expression: n√x

* Each of the parts of the expression n√x has specific names; m is the index of the