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Solutions
Solutions

NESTED INTERVALS
NESTED INTERVALS

Big Picture Day: Slopes of Tangent Lines and Derivative Techniques
Big Picture Day: Slopes of Tangent Lines and Derivative Techniques

Activities - WVU Math Department
Activities - WVU Math Department

General Power Functions
General Power Functions

This packet contains the topics that you have learned in your
This packet contains the topics that you have learned in your

... Summer work for Trigonometry and Pre- Calculus ...
Section 5.1 - The First Derivative
Section 5.1 - The First Derivative

... From previous lectures we can recall the following facts about the first derivative: Consequently, we ...
Calculus Fall 2010 Lesson 26 _Optimization problems_
Calculus Fall 2010 Lesson 26 _Optimization problems_

Chapter 4 Review Worksheet
Chapter 4 Review Worksheet

... 1) F is a linear function for which F(4)=6 and F(-3)=5. Find the equation for the function F. Find F(12) 2) Does the function g ( x)  17  6 x  x 2 have a maximum or a minimum value? What is that value? Problems 3 – 4: Convert the equation into standard form for a parabola. Find the vertex, x and ...
PDF
PDF

... For all other positive integers the value of Carmichael’s function is the least common multiple of all the dividing primes raised to the appropriate powers (e.g., to calculate ψ(504) we’d reckon ψ(23 ), ψ(32 ) and ψ(7) and find the LCM of these). Sequence A002322 in Sloane’s OEIS gives values of ψ(n ...
exponential and logarithm functions and derivatives: 1.logarithms
exponential and logarithm functions and derivatives: 1.logarithms

Lecture Slides
Lecture Slides

... Copyright © Cengage Learning. All rights reserved. ...
File
File

... If even one of these conditions is not met, then the function is discontinuous. Example 1: At which numbers is f discontinuous? Why? Solution: Continuity from the Left/Right A function may have a point of discontinuity but still be considered continuous from either the left or the right. f ( x)  f ...
Asymptotic and unbounded behavior
Asymptotic and unbounded behavior

2.2B Graphing Quadratic Functions in Standard Form
2.2B Graphing Quadratic Functions in Standard Form

Popper 03 Question 5
Popper 03 Question 5

Delta Function and the Poisson Summation Formula
Delta Function and the Poisson Summation Formula

Limits and Continuity
Limits and Continuity

algebraic formula of function
algebraic formula of function

3.2 - The Growth of Functions
3.2 - The Growth of Functions

Section 3.1 Extrema on an Interval Definition of Relative Extrema
Section 3.1 Extrema on an Interval Definition of Relative Extrema

xx - UTEP Math
xx - UTEP Math

Original
Original

... shown in the following figure. It is important to recognize that the point (0, 0) is on ...
PDF
PDF

Assignment 9 (for submission in the week beginning 5
Assignment 9 (for submission in the week beginning 5

... (b) Does every polynomial of degree greater 2 have a fixed point? Give reasons for your answer. 7 (Project) Let r be an irrational real number greater than 1. The Beatty sequence Br is the sequence of natural √ numbers whose nth term is bnrc. For example, if r = 2 = 1.41421 . . ., then the terms of ...
< 1 ... 125 126 127 128 129 130 131 >

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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