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Special Sequences and Series
Special Sequences and Series

Oct. 4 3.3 Continuous-Type Random Variables Oct. 4 3.3
Oct. 4 3.3 Continuous-Type Random Variables Oct. 4 3.3

... Oct. 4 ...
476 Chapter 8: Techniques of Integration (which converges) using
476 Chapter 8: Techniques of Integration (which converges) using

Lecture on Using Derivatives to Find Functional Behaviors
Lecture on Using Derivatives to Find Functional Behaviors

Properties of Functions New Functions from Old
Properties of Functions New Functions from Old

... Problem. Use the equation y = x 2 −3x + 2 to answer these questions about the function y = f(x). 1. For what values of x is y = 0? 2. For what values of x is y≥ 0 ? 3. Does y have a maximum and minimum value? If so find them and the x for which they occur. 4. For what values of x is y = −5? Solutio ...
An Introduction to Functions
An Introduction to Functions

...  Arithmetic Sequence – the difference between consecutive terms is constant  Common Difference – the difference between consecutive terms  Recursive Formula – a function rule that relates each term of a sequence after the first to the ones before it ...
these two pages
these two pages

§4 谓词演算的性质
§4 谓词演算的性质

The Definite Integral - USC Upstate: Faculty
The Definite Integral - USC Upstate: Faculty

Full text
Full text

... where / ( / ) is a differentiate function defined on the real number interval [a, b), and x may be a real or complex number with x*0 and x*l. Obviously, the case for x = l of (1.1) could be generally treated by means of the well-known Euler-Maclaurin summation formula. The object of this paper is to ...
Absolute Value Bivariate Data Domain Algebraic Expression
Absolute Value Bivariate Data Domain Algebraic Expression

... More terms may be found at http://www.k12.wa.us/Mathematics/TestItemSpec.aspx. ...
DEPARTMENT OF MATHEMATICS
DEPARTMENT OF MATHEMATICS

section 2.1- rates of change and limits
section 2.1- rates of change and limits

HERE
HERE

... Mathematical terms have precise meanings. The symbol “-“ is commonly read as both negative and opposite. However, a negative number is a kind of number, while the opposite of a number describes the relationship of one number to another. For example, negative 6 (-6) indicates a number < 0, and the nu ...
Revised Version 070427
Revised Version 070427

ITrig 2.4 - Souderton Math
ITrig 2.4 - Souderton Math

... We have talked about the look of a 2nd degree equation and we have called it a parabola. Here are some characteristics. 1. The domain is all real numbers, and the range is either (, max) or (min, ) . 2. If the coefficient of x 2 is positive, it opens up and if the coefficient is negative, it ope ...
document
document

SAT MATH PREPERATION
SAT MATH PREPERATION

... • Multiply x on both sides to get 5 = (5 + a)*x/(x + a) • Multiply (x + a) on both sides to get 5(x + a) = x*(5 + a) • Simplify to get 5x + 5a = 5x + x*a • 5a – x*a = 0 ...
FUNCTIONS Section 3.1 to 3.3
FUNCTIONS Section 3.1 to 3.3

Mathathon Round 1 (2 points each) 1. A circle is inscribed inside a
Mathathon Round 1 (2 points each) 1. A circle is inscribed inside a

Your Name Goes Here
Your Name Goes Here

... (a) The set of all integers greater than or equal to 5. (b) The set of all even integers. (c) The set of all positive rational numbers. (d) The set of all real numbers greater than 1 and less than 7. (e) The set of all real numbers whose square is greater than 10. 4. LATEX (2.4.12) The following exe ...
Dirichlet Series - MFO, Oberwolfach
Dirichlet Series - MFO, Oberwolfach

Systems Approach to Recursion
Systems Approach to Recursion

... Systems of equations may also be applied to finding the closed recursive (or explicit) form of a function. The recursive requires that we know the previous value in a sequence to find the subsequent. For instance: Consider the sequence 4, 7, 10, 13, 16, … We can see immediately that the values are c ...
Here
Here

< 1 ... 119 120 121 122 123 124 125 126 127 ... 132 >

Non-standard calculus

In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.Calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians like Richard Courant viewed infinitesimals as being naive and vague or meaningless.Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Jerome Keisler, ""Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century.""
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