Calculus | Mathematical terminology
In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the propensity of assuming different values). The term can take on several different meanings depending on the context. For example: * In various branches of mathematics, certain concepts are introduced as primitive notions (e.g., the terms "point", "line" and "angle" in geometry). As these terms are not defined in terms of other concepts, they may be referred to as "undefined terms". * A function is said to be "undefined" at points outside of its domain – for example, the real-valued function is undefined for negative (i.e., it assigns no value to negative arguments). * In algebra, some arithmetic operations may not assign a meaning to certain values of its operands (e.g., division by zero). In which case, the expressions involving such operands are termed "undefined". (Wikipedia).
Ratios with zeros - a problem for many early math students. This video helps you understand how to derive those values.
From playlist Summer of Math Exposition Youtube Videos
This algebra video provides a basic introduction into vertical lines and their undefined slopes. The slope of a horizontal line, on the other hand, is zero.
From playlist New Algebra Playlist
In this video, we we find the values of x that lead to an undefined result.
From playlist Algebra 2 Chapter 1 Take Home Test
A15 More about undetermined coefficients
A more complex example of a linear set of differential equations solved by the technique of variation of parameters.
From playlist A Second Course in Differential Equations
Graph simple inequalities on a number line.
From playlist Algebra: Linear Equations with One Variable
Limit doesn't exist 2 variables example
Example of how to show a limit doesn't exist for a function of 2 variables.
From playlist Engineering Mathematics
I relate the languages of "wondrous wisdom" and "advanced mathematics". As an example, I express the mental framework of One, All, Many with the minimization operator μ from computability theory. (This example starts at 8:45, ends at 43:00, and is the part that is relevant for the SOME2
From playlist Summer of Math Exposition 2 videos
Calculus: What is zero to the power of zero?
This mathematics video discusses the question of what is 0^0 (zero to the power of zero) and explains the two reasonable answers to this question.
From playlist Math talks
Want to PASS Algebra? Know how to answer this: Given f(x)= 4x +1/3x-9, what is f(3)?
How to find the domain of a function. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All course
From playlist GED Prep Videos
Difficulties with real numbers as infinite decimals ( I) | Real numbers + limits Math Foundations 91
There are three quite different approaches to the idea of a real number as an infinite decimal. In this lecture we look carefully at the first and most popular idea: that an infinite decimal can be defined in terms of an infinite sequence of digits appearing to the right of a decimal point
From playlist Math Foundations
Critical Numbers of f(x) = 1/x
In this video we find the critical numbers, if any, of the function f(x) = 1/x. Recall that critical numbers are numbers in the domain of the function where the derivative is zero or undefined. Great Calculus Book: https://amzn.to/3VfotAU This is my affiliate link. As an Amazon Associate
From playlist Critical Numbers
Algebra - Ch. 10: Rational Expressions (3 of 35) When is a Rational Expression Undefined?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give an example of what is the principle of a rational expression. We can only simplify a rational expression if we can factor the same factor from both the numerator and the denominator.
From playlist ALGEBRA CH 10 RATIONAL EXPRESSIONS
Undefined and indeterminate | Functions and their graphs | Algebra II | Khan Academy
Why 0/0 is considered to be indeterminate Watch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/new_operators/v/new-operator-definitions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Missed the previous lesson? https://www.khanacademy.org/math/alge
From playlist Algebra Foundations
Geometric Algebra, First Course, Episode 03: Relative Magnitudes and Scalars.
We grow our Vector to be a Scalar + Vector as we examine how to divide a geometric quantity by another. We see that it is OK to divide quantities that have the same aspect ("direction") even though we don't know how to calculate absolute magnitudes.
From playlist Geometric Algebra, First Course, in STEMCstudio
Calculus 1: Lecture 3.1 Extrema on an Interval
This is a real classroom Calculus 1 lecture. In this lecture I covered section 3.1 which is Extrema on an Interval. We talked about critical numbers, the extreme value theorem, and various other things. Lots of examples were done. I hope this helps someone.
From playlist Calculus 1 Full Lectures
Algebra 1 2.09d - Rules for Division
Further discussion of rules for division. This video discusses dividing zero by a number, dividing a number by zero (not allowed!), and also the fact that division is not commutative and is not associative. Examples are included. From chapter 2 of the Algebra 1 course by Derek Owens.
From playlist Algebra 1 Chapter 2 (Selected Videos)
Zorn's Lemma, The Well-Ordering Theorem, and Undefinability (Version 2.0)
Zorn's Lemma and The Well-ordering Theorem are seemingly straightforward statements, but they give incredibly mind-bending results. Orderings, Hasse Diagrams, and the Ordinals / set theory will come up in this video as tools to get a better view of where the "proof" of Zorn's lemma comes f
From playlist The New CHALKboard
Using Graphs with Linear Functions
Evaluate linear functions from their graphs. Draw the graph of a linear function. Write the equation of a linear function from its graph.
From playlist Algebra 1
Domain of a Rational Expression 1
u15_L1_T1_we1 Domain of a Rational Expression 1
From playlist Developmental Math 3