# #calculus

In this video I go over the definitions and notations involved in combining two different functions. What I mean by combining functions, I mean adding, subtracting, multiplying and dividing two functions.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/combination-of-functions

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/combination-of-functions

Related Videos:

Types of Intervals - Closed vs Open Intervals: http://youtu.be/wGthQDEixcw .

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1 day, 21 hours ago

In this video I go over another Applied Project and titled “Radiation from the Stars”. This is an interesting project from my calculus book at the end of the section on Infinite Sequences and Series. The project involves blackbody radiation and comparing the classical model with the newer quantum mechanics model.

Blackbody radiation is the heat radiation of a simplified ideal object that absorbs all incoming radiation and emits radiation that is dependent only on temperature of the object and not the frequency of the incoming radiation. Objects such as a furnace blast, matte black, and superheated objects like the Sun behave as blackbody radiators.

In the 19th century, John William Strutt aka “Lord Rayleigh” and James Jeans had derived a theoretical model for the radiation spectrum of a blackbody, but this diverged significantly from known experimental findings, in particular at low wavelengths or high frequency light. This resulted in what is known as the Ultraviolet Catastrophe.

In 1900, Max Planck looked to resolve this by postulating that light can only exist in discrete packets or quanta and not at any arbitrary value. This quantization of light produced experimentally accurate results for blackbody radiation and ushered in the start of “Quantum Mechanics”.

In this particular Applied Project, I go over Planck’s Law, determine its limits, and show that at high wavelengths the law converges to Rayleigh-Jeans Law.

Later in the video I make a note regarding Planck’s Constant and a potentially better interpretation of the quantization of energy from the YouTuber Lori Gardi aka Fractal Woman. I had initially written up a more extensive derivation of Planck’s Law in this video, but I have since removed it to do as a separate video in the future. Nonetheless, I have included the following links for further research:

- Derivation of Planck’s Law by “Physics Explained”: https://youtu.be/rCfPQLVzus4
- Interpretation of Plank’s Constant by “Fractal Woman”: https://peakd.com/hive-128780/@mes/cycles-planck-s-constant-and-the-true-nature-of-light

The topics covered in this video are listed below with their time stamps.

- @ 0:00 – Intro
- @ 1:34 - MES Note: Sharpen Your Mind with Mathematics
- @ 3:31 - Calculus Book Reference
- @ 3:45 - Topics to Cover
1. @ 4:16 - Note on Applied Projects
2. @ 4:37 - Applied Project: Radiation from the Stars
- @ - 13:23 - 5 Questions
3. Solutions
- @ 15:44 - Solution to Question 1
- @ 40:33 - Solution to Question 2
- @ 51:00 - Solution to Question 3
- @ 56:04 - Solution to Question 4
- @ 56:44 - Solution to Question 5
4. @ 1:02:08 - Quick Review of Planck's Law
- @ 1:11:28 - MES Note on Planck's Constant

3 weeks, 3 days ago

7-minute Calculus concepts - Derivatives concept quiz in 7 minutes

1 month ago

5-minute Calculus concepts - Limit concept quiz in 5 minutes

1 month ago

5 minute Calculus - Numerical Integration (left and right Riemann sum, trapezoid, midpoint, Simpson's) in 5 minutes and the questions relate to approximation and error bounds
-
(1) Approximate integral of 1/x from 1 to 2 with n=4 using the five numerical integration techniques
(2) For the approximation to be within 0.0001 of the integral value I, what should n be for T, M, and S?

1 month ago

Free-response question:
1) How do solution curves differ between exponential growth and logistic growth?
2) Solve the generic logistic growth differential equation
3) What is the size of the population when the growth is the fastest

1 month ago

Find the first four (non-zero) terms of the Maclaurin series for sin^2(x) and cos^2(x)
--by squaring the series for sin (x)
--by power reduction formula
--by calculating coefficients using the definition

1 month ago

Free response question on derivative function
1) On what intervals is f(x) (i) positive or negative, (ii) increasing or decreasing, or (iii) concave up or down?
2) Find the points for the four kinds of extrema for f(x)
3) Sketch f(x)
-
Questions are my own and are based upon the most common questions for that topic in the AP* exam. The questions are NOT official, but they relate to topics in the official test. (*AP is a trademark [registered / owned] by the College Board, which is not affiliated with, and does not endorse, these videos)

1 month, 2 weeks ago

Free response question on particle:
1) Find the zeroes of position p (t), velocity v (t), and acceleration a (t)
2) What is the average position p (t), velocity v (t), and acceleration a (t) between t_1 = 0 and t_2 = 4?
3) When is speed increasing or decreasing? What is the average speed between t_1 = 0 and t_2 = 4?
4) What is the total distance travelled by the particle from t_1 = 0 to t_2 = 4?
--
Questions are my own and are based upon the most common questions for that topic in the AP* exam. The questions are NOT official, but they relate to topics in the official test. (*AP is a trademark [registered / owned] by the College Board, which is not affiliated with, and does not endorse, these videos)

1 month, 2 weeks ago

Free response question:
1) Sketch the curve of the cardioid
2) Find the area outside the cardioid and inside the circle
3) What is the perimeter of the cardioid
4) What are points where there are vertical and horizontal tangent lines
-
Questions are my own and are based upon the most common questions for that topic in the AP* exam. The questions are NOT official, but they relate to topics in the official test. (*AP is a trademark [registered / owned] by the College Board, which is not affiliated with, and does not endorse, these videos)

1 month, 2 weeks ago

Free response question:
1) Sketch the curve of the cycloid
2) Where are tangents horizontal? Vertical?
3) What is the area under one arch of the cycloid?
4) What is the length of one arch of the cycloid
--
Questions are my own and are based upon the most common questions for that topic in the AP* exam. The questions are NOT official, but they relate to topics in the official test. (*AP is a trademark [registered / owned] by the College Board, which is not affiliated with, and does not endorse, these videos)

1 month, 2 weeks ago

Free response question on accumulation function
1) On what intervals is g(x) (i) positive or negative, (ii) increasing or decreasing, or (iii) concave up or down?
2) Find the x-values for the four kinds of extrema for g(x)
3) Sketch g(x)
--
Questions are my own and are based upon the most common questions for that topic in the AP* exam. The questions are NOT official, but they relate to topics in the official test. (*AP is a trademark [registered / owned] by the College Board, which is not affiliated with, and does not endorse, these videos)

1 month, 2 weeks ago

In this video I go through another problems plus example which in this case is on Mathematical Induction. I also go over mathematical induction is and use the tough problems plus example to illustrate it further. The principle of mathematical induction is pretty straight forward but the wording of it can be a bit tricky. Basically it states that if your function is true for n = 1, and it's true for k+1 if at k is true then it is true for all positive integers n. Since n = 1 is true, it follows that n = 2 is true and thus n = 3 and so on forever.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/problems-plus-example-4-mathematical-induction

Related Videos:

Problems Plus Example 1: http://youtu.be/YjoV9TLICOI
Problems Plus - Example 2: Solve hypotenuse in terms of the Perimeter: http://youtu.be/kvtjSQ2g1UE
Problems Plus - Example 3: |x-3| + |x+2| less than 3: http://youtu.be/EdQBtuo2gqM
Composition of functions: http://youtu.be/8HJE47q7-pA .

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2 months, 1 week ago

In this video I do I a brief overview on the limit laws which are basically properties of limits. I also show how you can easily remember them by stating them verbally. Basically the limit of a difference/sum/product/quotient is just the difference/sum/product/quotient of the limits. Make sure you watch this video and keep in mind these limit laws. In later videos I will provide some examples as well as proofs for all the laws shown in this video.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-laws-part-1-brief-overview

Related Videos:

One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
Math Paradoxes: Limits and Infinite Sums: http://youtu.be/Uq-8CGkyyqE
The Limit of a Function: http://youtu.be/0RX1o7KeZ28 .

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2 months, 4 weeks ago

In this video I go through further laws which will enable us to apply the first 5 laws shown in my earlier video. Also, since my calculus book included a section on the history of limits and Isaac Newton's involvement in the explicit formulation of limits, I thought it would be good to go over the history of Limits and how it has developed over the years. If you are interested in how the basic concepts of calculus began, make sure you watch this video!

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-laws-part-2--brief-history-of-newton-and-limits

Related Videos:

Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 1 Examples: http://youtu.be/tL_c7ZKkUBQ
One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
Math Paradoxes: Limits and Infinite Sums: http://youtu.be/Uq-8CGkyyqE
The Limit of a Function: http://youtu.be/0RX1o7KeZ28
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk .

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3 months ago

In this video I go through some useful examples in illustrating how to apply the limit laws which were discussed in my earlier videos. Also I introduce the direct substitution property which allows for directly solving limits of polynomial and rational functions. I will do more examples on cases where direct substitution does not apply in later videos so stay tuned!

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-laws-examples--intro-to-direct-substitution-property

Related Videos:

Rational and Algebraic Functions - A Brief Explanation: http://youtu.be/4mvNTeXEW-k
Polynomials - A Simple Explanation: http://youtu.be/IHIh7Y0kStE
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 1 Examples: http://youtu.be/tL_c7ZKkUBQ
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs .

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3 months, 1 week ago

In this video I go over briefly what the direct substitution property is for limits and also go over a very useful example on how to solve limits where you can't directly substitute numbers into the limit.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limits-where-direct-substitution-doesnt-work

Related Videos:

Rational and Algebraic Functions - A Brief Explanation: http://youtu.be/4mvNTeXEW-k
Polynomials - A Simple Explanation: http://youtu.be/IHIh7Y0kStE
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 1 Examples: http://youtu.be/tL_c7ZKkUBQ
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws Part 2 - Examples + Intro to Direct Substitution Property: http://youtu.be/cIjWhV7YdOE
Limits - Examples Part 1: http://youtu.be/lczWvRBw60A .

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3 months, 1 week ago

In this video I go further into the wonderful world of limits and solve some useful examples utilizing the concepts of limits which I went over in my earlier videos. These examples are useful in understanding how to solve different cases of limits that might arise so make sure to watch this video!

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limits-examples-part-1

Related Videos:

Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 1 Examples: http://youtu.be/tL_c7ZKkUBQ
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws Part 2 - Examples + Intro to Direct Substitution Property: http://youtu.be/cIjWhV7YdOE
Limits - where Direct Substitution doesn't work: http://youtu.be/L9jrwf-IKeU
The Limit of a Function: http://youtu.be/0RX1o7KeZ28
Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ .

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3 months, 1 week ago

In this video I continue on the Limits Examples series and do a pretty interesting example on the Greatest Integer Function. The greatest Integer function can usually be written as [[x]] or |_x_| and it simply means that it is gives the largest integer less than or equal to x.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limits-examples-part-3-greatest-integer-function

Related Videos:

Types of Numbers: Natural, Integers, Rational, Irrational, and Real Numbers: http://youtu.be/U22Z1q_Ibqg
Limits - Examples Part 1: http://youtu.be/lczWvRBw60A
Limits - Examples Part 2 - One Sided Limits Approach: http://youtu.be/9O6UFASe4F8
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 1 Examples: http://youtu.be/tL_c7ZKkUBQ
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws Part 2 - Examples + Intro to Direct Substitution Property: http://youtu.be/cIjWhV7YdOE
Limits - where Direct Substitution doesn't work: http://youtu.be/L9jrwf-IKeU .

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3 months, 2 weeks ago

In this video I continue further into finding the period of trigonometric functions and look at a few harder examples. Although they appear harder, the concept and methodology of finding the period is the exact same as in Part 1.

Related Videos:

Finding Periods of Trig Functions - Examples Part 1: http://youtu.be/lBLa4D2pLlg
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Transformation of Functions Part 1: Vertical and Horizontal Shifts: http://youtu.be/CBZd19GFOTE
Transformations of Functions Part 2: Horizontal Stretching and Reflecting: http://youtu.be/8sUgreHjTt8 .

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3 months, 2 weeks ago

Earlier on I showed what the direct substitution property is and how it can be applied to solve limits involving polynomials or rational functions very easily. In this video I go over a simple proof for the direct substitution property for polynomials using the limit laws, which I have also gone over in my earlier videos. In later videos I will provide precise proofs for all the limit laws used in this video.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/direct-substitution-for-polynomials-simple-proof

Related Videos:

Limit Laws - Part 1 Examples: http://youtu.be/tL_c7ZKkUBQ
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws Part 2 - Examples + Intro to Direct Substitution Property: http://youtu.be/cIjWhV7YdOE
Limits - where Direct Substitution doesn't work: http://youtu.be/L9jrwf-IKeU
Limits - Examples Part 1: http://youtu.be/lczWvRBw60A
Limits - Examples Part 2 - One Sided Limits Approach: http://youtu.be/9O6UFASe4F8
Polynomials - A Simple Explanation: http://youtu.be/IHIh7Y0kStE .

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3 months, 3 weeks ago

In this video I continue further into the Direct Substitution Property for Limits and prove that it's true for rational functions while utilizing the same property for polynomials (which was proved earlier).

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/direct-substitution-for-rational-functions-simple-proof

Related Videos:

Direct Substitution for Polynomials - Simple Proof: http://youtu.be/Fnb72ERTLqY
Rational and Algebraic Functions - A Brief Explanation: http://youtu.be/4mvNTeXEW-k
Limit Laws - Part 1 Examples: http://youtu.be/tL_c7ZKkUBQ
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws Part 2 - Examples + Intro to Direct Substitution Property: http://youtu.be/cIjWhV7YdOE
Limits - where Direct Substitution doesn't work: http://youtu.be/L9jrwf-IKeU
Limits - Examples Part 1: http://youtu.be/lczWvRBw60A
Limits - Examples Part 2 - One Sided Limits Approach: http://youtu.be/9O6UFASe4F8
Polynomials - A Simple Explanation: http://youtu.be/IHIh7Y0kStE .

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3 months, 3 weeks ago

In this video, I go over what a difference of squares are and derive the equation to easily factor them. It is very simple so make sure you memorize it as difference of squares are sure to come up in most math/engineering/physics classes you take and it can greatly simplify your work.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/factoring-difference-of-squares

Related Videos:

Factoring Quadratic Polynomials by Guessing: http://youtu.be/biEfGwT5pn4
Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ
Completing the Square: http://youtu.be/5uxV6-f_qc0
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0
Power Functions Part 2: What is x^0 and 0^0???: http://youtu.be/VzFUDiLzRiE .

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3 months, 3 weeks ago

In this video, I go over a very simple but very important concept known as rationalizing the denominator. This basically changes the denominator from an irrational number to a rational one. This can greatly simplify functions and sometimes this method is necessary when dealing with limits where the denominator is equal to 0. So make sure to watch this video!

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/rationalizing-the-denominator

Related Videos:

Factoring: Difference of Squares: http://youtu.be/qFdohskRQB0
Types of Numbers: Natural, Integers, Rational, Irrational, and Real Numbers: http://youtu.be/U22Z1q_Ibqg
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0 .

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3 months, 4 weeks ago

In my earlier videos I went over limits and limit laws but through a intuitive definition that used subjective terms such as "close to a" but that is not good enough to prove conclusively some limits especially limits that don't have the direct substitution property. In this video I go over the precise definition of a limit as well as going through a simple example to better illustrate it. This concept is more abstract and complex but it is necessary to make defining the limit more concrete. This is very important to understand as it is the building block for calculus so make sure to watch this video!

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/precise-definition-of-a-limit

Related Videos:

What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
The Limit of a Function: http://youtu.be/0RX1o7KeZ28
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws Part 2 - Examples + Intro to Direct Substitution Property: http://youtu.be/cIjWhV7YdOE
Limits - where Direct Substitution doesn't work: http://youtu.be/L9jrwf-IKeU
Absolute Values - Properties and Rules: http://youtu.be/tl9iten87MU .

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4 months ago

In my earlier videos I went over how to precisely define and prove the limits of a function in general. In this video I use the same concept but look at one sided limits and how to precisely define them. The concept is pretty much the same as for general limits.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/precise-definition-of-one-sided-limits

Related Videos:

One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
Limits - Examples Part 2 - One Sided Limits Approach: http://youtu.be/9O6UFASe4F8
Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq
Precise Definition of a Limit - Example 1: http://youtu.be/p__GkKUswmY
Precise Definition of a Limit - Example 2: Proving limits exists: http://youtu.be/HC-ClOx1sFs .

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4 months ago

In this video I continue with the wonderful world of limits and go over a more difficult example using the precise definition of a limit. In this case I show how to prove the limit of x^2 as x approaches 3 is equal to 9 using a pretty clever method. For more complicated functions, using the precise definition to prove limits becomes increasingly more difficult. But luckily we can simply prove them using the limit laws which I went over in my earlier videos (see video links below). But those limit laws need to be proven and I will prove each one in my videos to come.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/precise-definition-of-a-limit-example-3

Related Videos:

Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq
Precise Definition of a Limit - Example 1: http://youtu.be/p__GkKUswmY
Precise Definition of a Limit - Example 2: Proving limits exists: http://youtu.be/HC-ClOx1sFs
Precise Definition of One Sided Limits: http://youtu.be/Zarz1_ehv84
Precise Definition of One Sided Limits - Example: http://youtu.be/IECI8QpGkzY
Factoring: Difference of Squares: http://youtu.be/qFdohskRQB0
Types of Intervals - Closed vs Open Intervals: http://youtu.be/wGthQDEixcw .

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4 months, 1 week ago

In this video I go over the proof for the Sum Limit Law using the precise definition of a limit. The sum law states that the limit of a sum is the sum of limits. This is used throughout to prove limits of functions so make sure to understand why it is in fact true.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-laws-proof-of-sum-law

Related Videos:

Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq
Precise Definition of a Limit - Example 1: http://youtu.be/p__GkKUswmY
Precise Definition of a Limit - Example 2: Proving limits exists: http://youtu.be/HC-ClOx1sFs
Triangle Inequality - Simple Proof: http://youtu.be/Q3wps6M6oB4
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg .

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4 months, 1 week ago

In this video I prove the Product Law which is the 4th Limit Law from my overview of Limit Laws video (see video link below). The Product Law states that the limit of a product is the product of limits. I prove this using the precise definition of a limit and although the proof may seem a bit abstract, it becomes much better to understand when you grasp fully the concept of the precise definition of a limit. So make sure to watch this video as well as the precise definition of a limit video (from the link below).

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-laws-proof-of-product-law

Related Videos:

Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq
Precise Definition of a Limit - Example 1: http://youtu.be/p__GkKUswmY
Precise Definition of a Limit - Example 2: Proving limits exists: http://youtu.be/HC-ClOx1sFs
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Proof of Sum Law: http://youtu.be/eZ13wOvSg64
Absolute Values - Properties and Rules: http://youtu.be/tl9iten87MU
Triangle Inequality - Simple Proof: http://youtu.be/Q3wps6M6oB4 .

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4 months, 2 weeks ago

In my last video I proved the limit law for limits using the precise definition of a limit and in this video I use that law to prove the constant multiple law. The constant multiple law basically states the limit of a constant times a function is the constant times the limit of the function. It is also a simple case of the product law, so the prove is pretty straight forward.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-laws-proof-of-constant-multiple-law

Related Videos:

Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws - Proof of Sum Law: http://youtu.be/eZ13wOvSg64
Limit Laws - Proof of Product Law: http://youtu.be/TNqTXJzqE7s .

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4 months, 2 weeks ago

In this video I go over a quick proof of the Difference Law for limits. The law states that the limit of a difference is the difference of limits. The proof involves using the sum and constant multiple laws. The proofs of these laws are shown in the video links below.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-laws-proof-difference-law

Related Videos:

Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Limit Laws - Part 2 + Brief History of Newton and Limits: http://youtu.be/K5n7y2BvnOs
Limit Laws - Proof of Sum Law: http://youtu.be/eZ13wOvSg64
Limit Laws - Proof of Product Law: http://youtu.be/TNqTXJzqE7s
Limit Laws - Proof of Constant Multiple Law: http://youtu.be/RJjyjrZlXQc .

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4 months, 2 weeks ago

In this video I go over the precise definition of an infinite limit for both positive and negative infinity. The definition is very similar to that of a general limit so make sure to watch the precise definition of a limit in the related videos below.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-limits-precise-definition

Related Videos:

Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq
Types of Intervals - Closed vs Open Intervals: http://youtu.be/wGthQDEixcw
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8 .

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4 months, 3 weeks ago

In my earlier video I went over the precise definition of infinite limits and in this video I illustrate it further by going over a useful example. The example I go over is trying to prove that the limit as x approaches 0 of 1/x^2 is infinite. Intuitively, it is easy to see why the limit is true but proving according to the precise definition is a bit more abstract but once you fully grasp the precise definition, proofs like this should be pretty straight forward.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-limits-precise-definition-example

Related Videos:

Infinite Limits - Precise Definition: http://youtu.be/QyVTgSzn7dE
Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq
Precise Definition of a Limit - Example 2: Proving limits exists: http://youtu.be/HC-ClOx1sFs
Types of Intervals - Closed vs Open Intervals: http://youtu.be/wGthQDEixcw
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Absolute Values - Properties and Rules: http://youtu.be/tl9iten87MU .

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4 months, 4 weeks ago

Last year I did an overview video on continuity and continuous functions but did not go through in too much detail so I have done just that in this video. In this video I go over what it means for a function to be continuous as well as illustrate several cases when a function is discontinuous or not continuous.

https://1drv.ms/b/s!As32ynv0LoaIiMpD5-WiMmjTno4_-A?e=U3Wj68

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/continuity

Related Videos:

Continuity and Open and Closed Intervals: http://youtu.be/u29fd3WYT-g
One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
Limits - Examples Part 2 - One Sided Limits Approach: http://youtu.be/9O6UFASe4F8
Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq .

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5 months ago

In this video I go over some very useful examples on continuity and show where and why discontinuities arise. I also go over the Greatest Integer Function in terms continuity and show that it has 'Jump' continuities.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/continuity-examples

Related Videos:

Continuity and Open and Closed Intervals: http://youtu.be/u29fd3WYT-g
One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
Limits - Examples Part 2 - One Sided Limits Approach: http://youtu.be/9O6UFASe4F8
Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq
Continuity: http://youtu.be/_tBGb7Ku-CM
Factoring Quadratic Polynomials by Guessing: http://youtu.be/biEfGwT5pn4
Limits - Examples Part 3: Greatest Integer Function: http://youtu.be/GG-2jHgDdOc .

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5 months ago

In this video I go further into the wonderful world of continuity and look at what it means for a function to be continuous on an interval and how to determine if it is indeed continuous.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/continuity-part-3-continuity-on-an-interval

Related Videos:

Continuity: http://youtu.be/_tBGb7Ku-CM
Continuity Examples: http://youtu.be/Wk88MAUFflk
Continuity Part 2 One Sided Continuity: http://youtu.be/1ehfKsXf3wE
Continuity and Open and Closed Intervals: http://youtu.be/u29fd3WYT-g
One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
Types of Intervals - Closed vs Open Intervals: http://youtu.be/wGthQDEixcw
Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I .

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5 months ago

In this video, I explore how you can determine the continuity of complicated functions by simply identifying basic functions that make them up and determining from them if they are continuous. I also show why all polynomials and rational functions are continuous everywhere (but in the case of rational functions, wherever they are defined).

https://1drv.ms/b/s!As32ynv0LoaIiMkec67RZpruBx9f4A?e=kttZ01

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/continuity-part-4-complicated-functions

Related Videos:

Continuity: http://youtu.be/_tBGb7Ku-CM
Continuity Examples: http://youtu.be/Wk88MAUFflk
Continuity Part 2 One Sided Continuity: http://youtu.be/1ehfKsXf3wE
Continuity Part 3: Continuity on an Interval: http://youtu.be/f760EuW42dg
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg
Direct Substitution for Polynomials - Simple Proof: http://youtu.be/Fnb72ERTLqY
Direct Substitution for Rational Functions - Simple Proof: http://youtu.be/sQa-HqgPonw .

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5 months, 1 week ago

The full video for this tutoring session available here: https://www.bitchute.com/video/W5Snat9LdGv6/

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VIDEO: ASMR Math #66: Calculus (29:45): Graphing Cubic Functions, Taking First & Second Derivative, How to
https://youtu.be/qpJA17_f-BA

VIDEO: ASMR Math: Completing The Square, Graphing Quadratic Functions, Parabolas, y=a(x-p)²+q - Male
https://youtu.be/DpORn0G2UK8

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Math, Drop in Tutoring Sessions: One-on-One Online Math Tutoring Sessions

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In Conversation with chycho: Q&A

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5 months, 1 week ago

In this video I go over the limit of a composite function theorem which states that if you have a function within another function then the limit can be written outside or within the main function. For example the limit of f(g(x)) equals f(limit of g(x)) as x approaches a. In the proof I used the precise definition of a limit make sure to fully understand it by watching the related videos in the links below.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-of-a-composite-function-theorem-proof

Related Videos:

Continuity: http://youtu.be/_tBGb7Ku-CM
Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rkq
Precise Definition of a Limit - Example 1: http://youtu.be/p__GkKUswmY
Precise Definition of a Limit - Example 2: Proving limits exists: http://youtu.be/HC-ClOx1sFs
Limit Laws - Proof of Sum Law: http://youtu.be/eZ13wOvSg64
Limit Laws - Proof of Product Law: http://youtu.be/TNqTXJzqE7s
Limit Laws - Proof of Constant Multiple Law: http://youtu.be/RJjyjrZlXQc
Limit Laws - Proof Difference Law: http://youtu.be/_rT1ZT10n-U
Limit Laws - Proof of Quotient Law: http://youtu.be/91D_6wru6G4 .

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5 months, 1 week ago

In this video I go over some useful examples on limits and continuity to better illustrate some of the theorems that I have covered in my earlier videos.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limits-and-continuity-examples

Related Videos:

Limit of a Composite Function Theorem: Proof: http://youtu.be/ymYg0VQbwtY
Continuity: http://youtu.be/_tBGb7Ku-CM
Continuity Examples: http://youtu.be/Wk88MAUFflk
Continuity Part 2 One Sided Continuity: http://youtu.be/1ehfKsXf3wE
Continuity Part 3: Continuity on an Interval: http://youtu.be/f760EuW42dg
Continuity Part 4: Complicated Functions: http://youtu.be/c4PSBgANFH8
Direct Substitution for Rational Functions - Simple Proof: http://youtu.be/sQa-HqgPonw
Factoring: Difference of Squares: http://youtu.be/qFdohskRQB0 .

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5 months, 2 weeks ago

In this video I go over a simple theorem on the continuity of composite function which when simply stated says that a continuous function of a continuous function is a continuous function. I also go over a few useful examples on the continuity of composite functions.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/continuity-of-composite-functions-examples

Related Videos:

Limit of a Composite Function Theorem: Proof: http://youtu.be/ymYg0VQbwtY
Continuity: http://youtu.be/_tBGb7Ku-CM .

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5 months, 3 weeks ago

In this video I go over what the intermediate value theorem is and show how it can be used to prove if a root of a function exists in any given interval.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/intermediate-value-theorem-example-on-proving-a-root-exists

Related Videos:

Rolle's Theorem: http://youtu.be/GYha-rqCaxY
Types of Intervals - Closed vs Open Intervals: http://youtu.be/wGthQDEixcw
Continuity: http://youtu.be/_tBGb7Ku-CM
Continuity Part 2 One Sided Continuity: http://youtu.be/1ehfKsXf3wE
Continuity Part 3: Continuity on an Interval: http://youtu.be/f760EuW42dg
Continuity Part 4: Complicated Functions: http://youtu.be/c4PSBgANFH8 .

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5 months, 3 weeks ago

In this video I go over infinite limits and what vertical asymptotes are in detail. In my earlier videos I have covered infinite limits and vertical asymptotes but have not gone in too much detail as I did in this video so make sure to watch this video!

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-limits-vertical-asymptotes

Related Videos:

What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
The Limit of a Function: http://youtu.be/0RX1o7KeZ28
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Slant Asymptotes - Guidelines to Curve Sketching: http://youtu.be/1pk9ZPPyXGo
One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
Infinite Limits - Precise Definition: http://youtu.be/QyVTgSzn7dE .

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5 months, 4 weeks ago

In my last video I went over infinite limits and vertical asymptotes in detail and in this video I illustrate them further by solving some very useful examples.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-limits-vertical-asymptotes-examples

Related Videos:

Infinite Limits - Vertical Asymptotes: http://youtu.be/H-5Txa8SOwQ
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Natural Logarithms, Log base 10, and Some Examples Using Logs: http://youtu.be/XRSkMk5L3pk
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0 .

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6 months ago

TIMESTAMP:
- Calculus, Graphing a Cubic Function begins at (29:45)
... and more... and apologies about the abrupt ending, the stream was interrupted.

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VIDEO: ASMR Math: Completing The Square, Graphing Quadratic Functions, Parabolas, y=a(x-p)²+q - Male
https://youtu.be/DpORn0G2UK8

***PLAYLISTS***

Math, Drop in Tutoring Sessions: One-on-One Online Math Tutoring Sessions

The Language of Mathematics

Math in Real Life

ASMR - Autonomous Sensory Meridian Response

10 by 10 Grid and Multiplication Table, plus a Math Puzzle, a Pattern Recognition Game (Includes Live Streams)

In Conversation with chycho: Q&A

Peace,

chycho

http://www.chycho.com

.

6 months ago

In this video I go over horizontal asymptotes in detail. Horizontal asymptotes arise as limits are taken to infinity and the function approaches a fixed number or limit without ever actually reaching it.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limits-at-infinity-horizontal-asymptotes

Related Videos:

Infinite Limits - Vertical Asymptotes: http://youtu.be/H-5Txa8SOwQ
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Slant Asymptotes - Guidelines to Curve Sketching: http://youtu.be/1pk9ZPPyXGo
Types of Intervals - Closed vs Open Intervals: http://youtu.be/wGthQDEixcw .

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6 months ago

In this video I go over further into infinite sequences and series, and this time look at the many applications of Taylor polynomials. When I was still a student in university, it was this particular concept of Taylor polynomials and their applications to all aspects of physics that got me interested in creating my Math Easy Solutions channel. And in this video I explore Taylor polynomials in approximating functions which can then be extended to most functions in physics.

The accuracy of our approximations can be determined using the Alternating Series Estimation theorem, Taylor's Inequality, and through graphical or even brute force calculation methods. The particular science and physics applications that I cover in this video include optics, electromagnetism, water waves, pendulums, and surveying.

The topics covered in this video are listed below with their time stamps.

- @ 1:04 - Topics to Cover
1. @ 2:18 - Introduction
- @ 2:48 - Recap on Power Series and Taylor Polynomials
2. @ 8:22 - Approximating Functions by Polynomials
- @ 30:37 - Example 1: f(x) = x^(1/3)
- Example 2: f(x) = sin x
- @ 53:48 - Using Alternating Series Estimation Theorem
- @ 1:14:22 - Using Taylor's Inequality
- @ 1:21:11 - Using Graphical Methods
3. @ 1:32:04 - Applications to Physics
- @ 1:32:38 - Example 3: Einstein's Theory of Special Relativity
- @ 2:02:16 - Optical Physics
4. @ 2:21:25 - Exercises
- @ 2:21:42 - Exercise 1: Taylor Derivatives
- @ 2:30:50 - Exercise 2: Optical Physics
- @ 3:19:35 - Exercise 3: Electric Dipoles
- @ 3:33:36 - Exercise 4: Water Waves
- @ 4:09:52 - Exercise 5: Pendulum Period
- @ 4:52:04 - Exercise 6: Surveying

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials

Related Videos:

Infinite Sequences and Series: Taylor and Maclaurin Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-taylor-and-maclaurin-series .

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6 months ago

TIMESTAMPS:
- What is Calculus? Introduction to Calculus (8:13)
- Cubic Function Problem, Graphing (16:14)
- Solving Systems of Equations (36:36)
- Discussion and Thought Experiment on Light (1:01:16)
- Why Learning Math is Important (1:17:17)
- Anime Discussion and Recommendation (1:30:20)
- Completing the Square (1:40:40)
- BEDMAS, Order of Operations, Isolating/Rearranging/Solving for a Variable (1:51:35)
... and more.

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VIDEO: Math in Art and Design: Using the Fibonacci Numbers to Create the Golden Rectangle (Real Life)
https://youtu.be/57BpoTAId8s

VIDEO: Math in Art and Design: The Golden Ratio, Rectangle, and Spiral - Dirk Marwig (Math in Real Life)
https://youtu.be/47d12EEeG54

VIDEO: ASMR Math: Completing The Square, Graphing Quadratic Functions, Parabolas, y=a(x-p)²+q - Male
https://youtu.be/DpORn0G2UK8

VIDEO: 11 Amazing Animated Series That Are Loop-worthy [ASMR, Best of]
https://youtu.be/Zj7U7R-2fcs

***PLAYLISTS***

Math, Drop in Tutoring Sessions: One-on-One Online Math Tutoring Sessions

The Language of Mathematics

Math in Real Life

ASMR - Autonomous Sensory Meridian Response

10 by 10 Grid and Multiplication Table, plus a Math Puzzle, a Pattern Recognition Game (Includes Live Streams)

In Conversation with chycho: Q&A

Peace,

chycho

http://www.chycho.com

.

6 months, 1 week ago

Last video I went over limits at infinity and horizontal asymptotes and in this video I illustrate those concepts further by going over some useful examples.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limits-at-infinity-horizontal-asymptotes-examples-part-1

Related Videos:

Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8 .

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6 months, 1 week ago

In this video I go over part 2 of examples series on horizontal asymptotes to illustrate further limits at infinity.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limits-at-infinity-horizontal-asymptotes-examples-part-2

Related Videos:

Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Limits at Infinity: Horizontal Asymptotes Examples Part 1: http://youtu.be/WtqQf6XEwJQ
L'Hospital's Rule and Indeterminate Forms - Intro: http://youtu.be/x-djc6wrY5w
Rationalizing the Denominator: http://youtu.be/fRb2TQQxH_Y .

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6 months, 1 week ago

In this video I go over another set of useful examples on horizontal asymptotes.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limits-at-infinity-horizontal-asymptotes-examples-part-4

Related Videos:

Limits at Infinity: Horizontal Asymptotes Examples Part 1: http://youtu.be/WtqQf6XEwJQ
Limits at Infinity: Horizontal Asymptotes Examples Part 2: http://youtu.be/2ENWSmkGMyg
Limits at Infinity: Horizontal Asymptotes Examples Part 3: http://youtu.be/NSusENiY3tk
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Exponential Functions and Graphing: http://youtu.be/FFNwh8KR9-Q .

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6 months, 2 weeks ago

In this video I look at infinite limits as x approaches either infinite or negative infinite. I also go over some very useful examples in dealing with infinite limits.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-limits-at-infinity-examples-part-1

Related Videos:

Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Limit Laws - Part 1: Brief Overview: http://youtu.be/qfk5c-43dLg .

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6 months, 2 weeks ago

In this video I go over more examples on infinite limits at infinity to better illustrate the concept. In one example I show how you can graph a function by knowing the x and y intercepts as well as the limits at infinity.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-limits-at-infinity-examples-part-2

Related Videos:

Infinite Limits at Infinity + Examples Part 1: http://youtu.be/qXLYInFkW7Y
Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Guidelines to Curve Sketching: http://youtu.be/tOn7ZSAntKs .

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6 months, 3 weeks ago

In this video I go over precise definition of a limit at infinity and negative infinity. Like my previous video on the precise definition of a limit, the concept is somewhat abstract but if you go over the video carefully, the definition is pretty straight forward.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/precise-definition-of-limits-at-infinity-horizontal-asymptotes

Related Videos:

Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rk
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Slant Asymptotes - Guidelines to Curve Sketching: http://youtu.be/1pk9ZPPyXGo
Infinite Limits at Infinity + Examples Part 1: http://youtu.be/qXLYInFkW7Y .

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6 months, 3 weeks ago

In this video I go over a very useful example to better illustrate the precise definition of limits at infinity, so make sure to watch this video!

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/precise-definition-of-limits-at-infinity-example-1

Related Videos:

Precise Definition of Limits at Infinity - Horizontal Asymptotes: http://youtu.be/hnjvmdU2j3w
Limits at Infinity: Horizontal Asymptotes Examples Part 2: http://youtu.be/2ENWSmkGMyg
Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rk
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Slant Asymptotes - Guidelines to Curve Sketching: http://youtu.be/1pk9ZPPyXGo
Infinite Limits at Infinity + Examples Part 1: http://youtu.be/qXLYInFkW7Y .

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6 months, 3 weeks ago

In this video I go over a second example on using the precise definition of limits at infinity to prove that the limit as x approaches infinity of the function 1/x equals 0.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/precise-definition-of-limits-at-infinity-example-2

Related Videos:

Precise Definition of Limits at Infinity - Horizontal Asymptotes: http://youtu.be/hnjvmdU2j3w
Precise Definition of Limits at Infinity: Example 1: http://youtu.be/YSS05S38MWU
Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rk
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Slant Asymptotes - Guidelines to Curve Sketching: http://youtu.be/1pk9ZPPyXGo
Infinite Limits at Infinity + Examples Part 1: http://youtu.be/qXLYInFkW7Y .

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6 months, 4 weeks ago

In this video I go over the precise definition of infinite limits as x approaches infinity. This is a pretty straight forward definition and is similar to my earlier videos on the precise definition of limits in general, and limits at infinity.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/precise-definition-of-infinite-limits-at-infinity

Related Videos:

Infinite Limits at Infinity + Examples Part 1: http://youtu.be/qXLYInFkW7Y
Precise Definition of Limits at Infinity - Horizontal Asymptotes: http://youtu.be/hnjvmdU2j3w
Precise Definition of a Limit: http://youtu.be/zOWuWE4M2rk
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Slant Asymptotes - Guidelines to Curve Sketching: http://youtu.be/1pk9ZPPyXGo .

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7 months ago

In this video I recap on the steps of calculating square roots by hand and go over steps involved in calculating the square root of 512.3 (which I calculated in my example 3 video).

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/calculating-square-roots-by-hand-overview

Related Videos:

Calculating Square Roots by Hand Example 1: (3)^(1/2): http://youtu.be/fJN8mmHxYcY
Calculating Square Roots by Hand Example 2: (72)^(1/2): http://youtu.be/gfpjvx5PNQc
Calculating Square Roots by Hand Example 3: (512.3)^(1/2): http://youtu.be/vAwf4jIk8C8
Long Division by Hand - An in depth look: http://youtu.be/giBZg5Vqryo
Multiplication by Hand - In depth look at the wonderful world of multiplication: http://youtu.be/bUKGh5R_0Sw
Addition and Subtraction by Hand - An in-depth look: http://youtu.be/Tkb7xU-lFWU
111,111,111 x 111,111,111 = 12345678987654321 - Hand Calculation: http://youtu.be/N1g-fe7ZxfA .

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7 months ago

In this video I go over a useful example on the definition of a derivative. I did a video on the definition of derivative just over a year ago and you can see that in the video link below.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/definition-of-derivative-example-1

Related Videos:

Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
The Limit of a Function: http://youtu.be/0RX1o7KeZ28 .

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7 months, 1 week ago

In this video I go over derivative notation and more specifically Leibniz notation. I also go over a brief biography of the genius and renaissance man, Gottfried Wilhelm Leibniz. From theology to politics to mathematics, Leibniz was very versatile in his studies and his version of calculus which was published in 1684 established the notation and rules for finding derivatives that we use today!

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivatives-notation-and-biography-of-leibniz

Related Videos:

Is the function Differentiable?? + Notation and Graphing of Derivatives: http://youtu.be/TjDApzC2D7I
Derivative as a function: Graphing Derivatives: http://youtu.be/9LOLieu4G3I
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk .

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7 months, 1 week ago

In many of my videos I have stated that the derivative can be viewed as the instantaneous rate of change of a function so I thought it would be good to do a video explaining further on this. In this video I go over how the derivative can be viewed as the instantaneous rate of change and show how the definition of instantaneous rate of change is the exact same as the definition of derivative.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/interpretation-of-the-derivative-as-rate-of-change

Related Videos:

Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Definition of Derivative: Example 1: http://youtu.be/5tFmJShACF4
Definition of Derivative: Example 2: http://youtu.be/Zo8YAbddCJI
What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
The Limit of a Function: http://youtu.be/0RX1o7KeZ28
Derivative Application: Deriving the Velocity from the Distance Function: http://youtu.be/3oT83konhlU .

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7 months, 1 week ago

In this video I go over a useful example on manufacturing costs to further illustrate interpreting the derivative as a rate of change of a function.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-as-rate-of-change-example-1-manufacturing-costs

Related Videos:

Interpretation of the Derivative as a Rate of Change: http://youtu.be/3nu6U-p6Ctg
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Marginal Cost vs Average Cost - Economics 101: http://youtu.be/HiMaLvsTstc
Marginal Cost vs Average Cost Example - Economics 101: http://youtu.be/W2xx0Wtl608
Marginal Cost vs Marginal Revenue: When is maximum profit realized??: http://youtu.be/ufMgmYbZPdU
Marginal Cost vs Marginal Revenue - Examples Part 1: Maximizing Profit: http://youtu.be/cQ83F5qynco
Marginal Cost vs Marginal Revenue - Examples Part 2: Maximizing Revenue : http://youtu.be/nrH_Jrpm7vU .

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7 months, 1 week ago

In this video I go over a useful example on the rate of change of the US National Debt in helping to better illustrate the derivative as a rate of change.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-as-rate-of-change-example-2-us-national-debt

Related Videos:

Interpretation of the Derivative as a Rate of Change: http://youtu.be/3nu6U-p6Ctg
Derivative as Rate of Change Example 1: Manufacturing Costs: http://youtu.be/LwZwkUBdWzg .

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7 months, 2 weeks ago

In this video I go over two methods on expanding the function (x+h)^3 to illustrate how to go about expanding functions with high powers. In the video I also go over a useful polynomial expanding calculator and you can view that calculator in the video link below.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/expanding-higher-power-functions

Related Videos:

Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ
Factoring: Difference of Squares: http://youtu.be/qFdohskRQB0
Rationalizing the Denominator: http://youtu.be/fRb2TQQxH_Y .

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7 months, 2 weeks ago

In this video I go over a general example on how to go about graphing the derivative of a function by interpreting it as the slope of that function.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-as-a-function-graphing-derivatives

Related Videos:

Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Definition of Derivative: Example 1: http://youtu.be/5tFmJShACF4
Definition of Derivative: Example 2: http://youtu.be/Zo8YAbddCJI
Interpretation of the Derivative as a Rate of Change: http://youtu.be/3nu6U-p6Ctg
Derivative as Rate of Change Example 1: Manufacturing Costs: http://youtu.be/LwZwkUBdWzg
Derivative as Rate of Change Example 2: US National Debt: http://youtu.be/f3G7k8_rK2s .

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7 months, 2 weeks ago

In this video I go over a useful example on determining the derivative or the rate of change of the population of Belgium when given a table of yearly population.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-as-a-function-example-1-population-growth

Related Videos:

Derivative as a function: Graphing Derivatives: http://youtu.be/9LOLieu4G3I
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Definition of Derivative: Example 1: http://youtu.be/5tFmJShACF4
Definition of Derivative: Example 2: http://youtu.be/Zo8YAbddCJI
Interpretation of the Derivative as a Rate of Change: http://youtu.be/3nu6U-p6Ctg
Derivative as Rate of Change Example 1: Manufacturing Costs: http://youtu.be/LwZwkUBdWzg
Derivative as Rate of Change Example 2: US National Debt: http://youtu.be/f3G7k8_rK2s .

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7 months, 3 weeks ago

Ever wonder how to calculate by square roots by hand?? I've always used a calculator to determine the square root of numbers that aren't perfect squares. And in this video I go over how to calculate the square root of 3 by hand. The method is pretty abstract but it is similar to long division and once you get the pattern down, it becomes pretty straight forward.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/calculating-square-roots-by-hand-example-1-3-1-2

Related Videos:

Long Division by Hand - An in depth look: http://youtu.be/giBZg5Vqryo
Multiplication by Hand - In depth look at the wonderful world of multiplication: http://youtu.be/bUKGh5R_0Sw
Addition and Subtraction by Hand - An in-depth look: http://youtu.be/Tkb7xU-lFWU
111,111,111 x 111,111,111 = 12345678987654321 - Hand Calculation: http://youtu.be/N1g-fe7ZxfA .

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7 months, 3 weeks ago

In this video I go over another example on calculating square roots by hand and calculate the square root of 512.3.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/calculating-square-roots-by-hand-example-3-512-3-1-2

Related Videos:

Calculating Square Roots by Hand Example 1: (3)^(1/2): http://youtu.be/fJN8mmHxYcY
Calculating Square Roots by Hand Example 2: (72)^(1/2): http://youtu.be/gfpjvx5PNQc
Long Division by Hand - An in depth look: http://youtu.be/giBZg5Vqryo
Multiplication by Hand - In depth look at the wonderful world of multiplication: http://youtu.be/bUKGh5R_0Sw
Addition and Subtraction by Hand - An in-depth look: http://youtu.be/Tkb7xU-lFWU
111,111,111 x 111,111,111 = 12345678987654321 - Hand Calculation: http://youtu.be/N1g-fe7ZxfA .

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7 months, 4 weeks ago

In this video I go over the Laboratory Project titled An Elusive Limit. Laboratory Projects are interesting math projects at the end of some sections of my calculus book, and in this case at the end of the section on Taylor and Maclaurin Series. The project I cover involves solving the limit of a function that has a difference in the numerator and denominator; and both include trigonometric sine and tangent functions, as we well as inverse trigonometric sine and tangent functions.

The interesting part of all of these functions is that as x approaches 0, then they all approach 0 in about the same rate so that their values are near identical to a high level of digits precision. This makes the resulting differences in the numerator and denominator of the function cancel out most of the digits and thus we are left with only a few correct decimal places. This makes the resulting calculations highly dependent on the level of precision of the calculator being used, and in most cases the calculator won’t be able to brute force calculate the function at values very close to x = 0.

In this case we can still solve the limit in several ways, either by using a computer algebra system (CAS) to solve derivatives or power series of the numerator and denominator, and thus be able to use methods such as l’Hospital’s Rule or other limit laws and algebra manipulation. This effectively means that if we can’t compute the function directly we can instead focus on simplifying or transforming the numerator and denominator into their equivalent but different formulations, which may allow for the limit to be solved through algebraic or calculus means.

This is a very interesting tutorial involving the use of calculators and understanding the levels of precision to be certain that the calculations are correct, so make sure to watch this video!

The topics covered in this video are listed below with their time stamps.

- @ 1:12 - Topics to Cover
1. @ 1:33 - Laboratory Project: An Elusive Limit
- 6 Questions
2. Solutions
- @ 3:13 - Solution to Question 1
- @ 19:51 - Solution to Question 2
- @ 21:14 - Solution to Question 3
- @ 28:40 - Solution to Question 4
- @ 41:12 - Solution to Question 5
- @ 43:13 - Solution to Question 6

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/laboratory-project-an-elusive-limit

Related Videos:

Laboratory Project: Logistic Sequences: https://peakd.com/mathematics/@mes/laboratory-project-logistic-sequences

Infinite Sequences and Series: Taylor and Maclaurin Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-taylor-and-maclaurin-series .

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8 months ago

In this video I go over another example to better illustrate the derivative as a function as well as in implementing the definition of the derivative. The example I go over is finding the derivative of the function y = x^3 - x.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-as-a-function-example-2-y-x-3-x

Related Videos:

Expanding Higher Power Functions: http://youtu.be/AG2eF5qaF74
Derivative as a Function: Graphing Derivatives: http://youtu.be/9LOLieu4G3I
Derivative as a Function Example 1: Population Growth: http://youtu.be/C4YVmZVUiNM
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Definition of Derivative: Example 1: http://youtu.be/5tFmJShACF4
Definition of Derivative: Example 2: http://youtu.be/Zo8YAbddCJI
Interpretation of the Derivative as a Rate of Change: http://youtu.be/3nu6U-p6Ctg .

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8 months ago

In this video I go over another example to better illustrate the derivative as a function as well as in implementing the definition of the derivative. The example I go over is finding the derivative of the function y = (x-1)^(1/2).

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-as-a-function-example-3-y-x-1-1-2

Related Videos:

Derivative as a Function: Graphing Derivatives: http://youtu.be/9LOLieu4G3I
Derivative as a Function Example 1: Population Growth: http://youtu.be/C4YVmZVUiNM
Derivative as a Function Example 2: y = x^3 - x: http://youtu.be/ADBIwRRkSqU
Rationalizing the Denominator: http://youtu.be/fRb2TQQxH_Y
Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Interpretation of the Derivative as a Rate of Change: http://youtu.be/3nu6U-p6Ctg .

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8 months, 1 week ago

I go back to TreeMC one last time to find my base. The area I set the coordinates to have become so unrecognisable. I've been informed about some shady tactics of pay to win model and ask some questions. These strange people thought I was talking about calculus for some reason.

8 months, 1 week ago

In this video I go over more advanced tests for convergence in order to determine the convergence or divergence of the Binomial Series at the endpoints. In particular, I first derive Kummer’s Test, which is a generalization of both the Ratio Test, covered in my earlier video, and Raabe’s Test, which I cover in this video. I also show that Raabe’s Test is essentially a test that compares series to the p-series, which I had covered before.

In my earlier video, I had covered the Binomial Series and showed using the Ratio Test that the radius of convergence was less than 1 but the test was inconclusive at the endpoints. This is where I use Raabe’s Test to overcome the shortcomings of the Ratio Test and show that at the endpoints, the Binomial Series may converge or diverge depending on the value of k. This is a pretty epic and extensive proof video, and likely far more thorough than any other proof found online, so make sure to watch it!

Note that Kummer’s Test was first obtained by German mathematician Ernst Eduard Kummer, while Raabe’s Test was obtained by Swiss mathematician Joseph Ludwig Raabe, and both during the mid-1800s.

Also note, that I obtained the proofs for Kummer’s Test and Raabe’s Test from a paper by Sarah Fix from Whitman College, USA. As for the Binomial Series proof, I used mainly the lecture PDF by John Labute from McGill University, Canada.

The topics covered in this video are listed below with their time stamps.

- @ 1:29 - Topics to Cover
1. @ 3:21 - Recap on the Ratio Test for Convergence
2. @ 5:18 - Advanced Tests for Convergence
- @ 6:06 - Kummer's Test
- @ 36:02 - Ratio Test is Kummer's Test with Bn = 1
- @ 43:07 - Note on Kummer's Test
- @ 43:38 - Raabe's Test: Kummer's Test with Bn = n
- @ 51:45 - Raabe's Test Compares Series to the p-Series
- @ 1:02:05 - Corollary of Raabe's Test
- @ 1:23:01 - Note on Raabe's Test and Kummer's Test
3. @ 1:24:04 - Recap on Power Series
- @ 1:26:40 - Taylor and Maclaurin Series
4. @ 1:27:32 - Recap on the Binomial Theorem
5. @ 1:29:59 - Recap on the Binomial Series
- @ 1:32:32 - Convergence at the Endpoints Depends on the Value of k
- @ 1:34:48 - Important Note on the Binomial Coefficients
6. @ 1:36:43 - Convergence of the Binomial Series
- @ 1:44:58 - Endpoint x = -1: Using Raabe's Test
- Converges when k is greater than 0
- Diverges when k is less than 0
- @ 2:01:43 - Endpoint x = 1: Alternating Series
- @ 2:07:37 - Using Raabe's Test: Absolute Convergence when k is greater than 0
- @ 2:12:34 - Using Alternating Series Test: Converges when k is between 0 and -1
- @ 2:42:53 - Pi Production Notation for Factorials
- @ 2:48:14 - Using Comparison Test: Diverges when k ≤ -1
- @ 2:58:30 - Can Also Use the Test for Divergence
- @ 2:59:12 - Trivial Case k = 0: Converges for all x
- @ 2:59:29 - Summary

---

Related Videos:

Representations of Functions as Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-representations-of-functions-as-power-series

Taylor and Maclaurin Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-taylor-and-maclaurin-series

Strategy for Testing Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-strategy-for-testing-series .

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8 months, 1 week ago

In this video I go over another example to better illustrate the derivative as a function as well as in implementing the definition of the derivative. The example I go over is finding the derivative of the function y = (1-x)/(2+x).

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-as-a-function-example-4-y-1-x-2-x

Related Videos:

Derivative as a Function: Graphing Derivatives: http://youtu.be/9LOLieu4G3I
Derivative as a Function Example 1: Population Growth: http://youtu.be/C4YVmZVUiNM
Derivative as a Function Example 2: y = x^3 - x: http://youtu.be/ADBIwRRkSqU
Derivative as a Function Example 3: y = (x - 1)^(1/2): http://youtu.be/ByANmgHhzfE
Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Interpretation of the Derivative as a Rate of Change: http://youtu.be/3nu6U-p6Ctg .

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8 months, 1 week ago

In this video I go over a very in-depth tutorial on division and multiplication of power series just as we would for polynomials. In my earlier video I had gone over an example on multiplying and dividing power series using the basic polynomial expansion and polynomial long division techniques, but I had not discussed the reasoning for why it works. In this video, however, I derive the power series that results from multiplying two power series and show that the resulting coefficients involve a “convolution” summation that can also be obtained in the same way had we just multiplied the power series as if they were polynomials.

The division of power series is effectively just the reverse of multiplication and thus to divide a power series is the same as figuring out which power series multiplies to get the numerator. I show that polynomial long division and double checking using multiplication yield the same result as expected.

Also in this video, I go over briefly on Euler’s identity and imaginary numbers to illustrate, in Example 3, that if we consider imaginary numbers then we need to account for when the denominator of a power series is equal to zero in the imaginary or complex set of numbers. This particular example was in regard to obtaining the power series of hyperbolic cosecant or csch.

The topics covered in this video are listed below with their time stamps.

- @ 1:14 - Topics to Cover
1. @ 2:19 - Recap on Power Series
- @ 5:54 - Taylor and Maclaurin Series
2. @ 6:59 - Recap on Earlier Example on Multiplication and Division of Power Series
3. @ 18:21 - Multiplication of Power Series
- @ 49:43 - Example 1: e^x/(1-x)
- @ 1:03:36 - Example 2: sin^2(x)
4. @ 1:27:37 - Division of Power Series
- @ 1:34:04 - Example 3: csch(x)
- @ 1:53:20 - Imaginary Numbers and Euler's Identity
- @ 2:02:08 - Double Checking Division By Multiplication

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-multiplication-and-division-of-power-series

Related Videos:

Infinite Sequences and Series: Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-power-series

Infinite Sequences and Series: Representations of Functions as Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-representations-of-functions-as-power-series

Infinite Sequences and Series: Taylor and Maclaurin Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-taylor-and-maclaurin-series"

Infinite Sequences and Series: Representations of Functions as Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-representations-of-functions-as-power-series

Leibniz’s Rule: Generalization of the Product Rule for Derivatives: https://peakd.com/hive-128780/@mes/leibniz-general-product-rule-for-derivatives

Polynomial Long Division - In depth Look on why it works! http://youtu.be/E1H584xJS_Y

Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ .

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8 months, 3 weeks ago

In this video I go over the theorem: If a function is differentiable then it is also continuous. This theorem basically means if the derivative exists at a, then it is also continuous at a. I also provide a simple proof using the definition of a derivative.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/a-differentiable-function-is-continuous-proof

Related Videos:

Is a function Differentiable? + Example: y = |x|: http://youtu.be/th51Xz7YmvI
Derivatives Notation and Biography of Leibniz: http://youtu.be/ROKtFQqJOBE
Continuity: http://youtu.be/_tBGb7Ku-CM
Continuity and Open and Closed Intervals: http://youtu.be/u29fd3WYT-g
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Is the function Differentiable?? + Notation and Graphing of Derivatives: http://youtu.be/TjDApzC2D7I .

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9 months ago

In this video I go over the 3 types of functions that are not differentiable. Those types are functions that have sharp corners, discontinuities, and infinite slopes.

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/functions-that-are-not-differentiable

Related Videos:

Is a function Differentiable? + Example: y = |x|: http://youtu.be/th51Xz7YmvI
A Differentiable Function is Continuous: Proof: http://youtu.be/l4Kzzppb_88
Is the function Differentiable?? + Notation and Graphing of Derivatives: http://youtu.be/TjDApzC2D7I
Continuity and Open and Closed Intervals: http://youtu.be/u29fd3WYT-g
Continuity: http://youtu.be/_tBGb7Ku-CM .

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