Math Easy Solutions

Math Easy Solutions

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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.

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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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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).

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiNcVX27-Gl9c4QBsuw?e=6L5p80

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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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiNZmBLHdFfaY0hvEoQ?e=FJM9am

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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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!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiNZKePMakigaNKhZ1A?e=89jUOE

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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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!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiNYkJxQAgOddjoF8hQ?e=yPOBE3

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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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiM00yUSc7RLk0hNDnw?e=ApYu5y

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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In my earlier video, I went over the precise definition of one sided limits and in this video I go over a useful example to show how you can prove the limit of a function using the precise definition. Make sure to also watch my videos on the general precise definition of limits and the examples on it in the video links below.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiM0HqMP67PpO4rpfrw?e=zI4le2

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

Related Videos:

Precise Definition of One Sided Limits: http://youtu.be/Zarz1_ehv84
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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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMxqJcCXle9g2lOtIQ?e=dYvf7M

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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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.

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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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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).

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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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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMwPFt89gBcniuedEg?e=W5o9Ks

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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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.

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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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I continue on the wonderful world of limit laws and prove the quotient law in this video. Basically the quotient law for limits states that the limit of a quotient is the quotient of a limits. The proof that I go through may seem a bit abstract but with a firm understanding of the precise definition of limits, it is pretty straight forward. So make sure to watch this as well as the videos on limits from the links below!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMtXK5DST_FrtrUN3Q?e=bE1QC8

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/limit-laws-proof-of-quotient-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
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
Absolute Values - Properties and Rules: http://youtu.be/tl9iten87MU
Triangle Inequality - Simple Proof: http://youtu.be/Q3wps6M6oB4 .

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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMsJzw1kpa5Ej6EKmQ?e=GXX9AU

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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Recently I tried graphing in Microsoft Excel but the data that I was graphing had some blank cells and thus the chart was not graphing it well. In this video I go over how Excel deals with graphing as well as calculating cells that include blanks and error values. I also show how you can use the #N/A error value to skip blanks when graphing as well as using the IF() and the ISERROR() functions to deal with calculating functions that include the #N/A (or NA() function) values. This is very important when you have to present data in charts using Excel so make sure to watch this video!

Download the notes in my video:

Excel File: https://1drv.ms/x/s!As32ynv0LoaIiMptX4xHHXZAFtVnrw?e=CoqYS5
PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIiMpyYZx2qpd-1yccUg?e=TZ3LvS

View video notes on the Hive blockchain: https://peakd.com/general/@mes/skip-blanks-when-graphing-in-microsoft-excel

Related Videos:

Convert Time to number, seconds, hours and minutes in Microsoft Excel 2007: http://youtu.be/fwMKbXI98tI
Converting Numbers to Fractions in Microsoft Excel 2007: http://youtu.be/YgJBK0QjIec
Drop Down Lists with Microsoft Excel 2007: http://youtu.be/e7Sbcn-y9j4
Can't copy and paste hyperlinks to Office Word?? Try Closing Internet Explorer: http://youtu.be/FczySOM59VQ
Showing Heading Levels in Table of Contents - Office Word 2007: http://youtu.be/psGZmT1mHzE .

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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMpY6mDC1Ty5x9I8IQ?e=IZWbA1

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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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.

Download the notes in my video:
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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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMopsd2zkM06HlQHNg?e=LnXf9F

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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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMlipxNk6EDcyJnaoQ?e=pvpggV

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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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).

Download the notes in my video:

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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In this video I go over how to easily make your Wordpress Website force that it gets viewed only in the desktop view instead of the mobile view on mobile devices such as phones, tablets, and other mobile devices. This is great if you do not have a decent mobile version of your website or just rather prefer that the desktop version be viewed on all operating systems.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMkBtDIva3sP5XW4oA?e=9NjM8C

View video notes on the Hive blockchain: https://peakd.com/wordpress/@mes/force-desktop-view-with-wordpress-website-on-mobile-devices

Learn more about the TeamViewer app I was using through their website: http://teamviewer.com

Related Videos:

Replace Samsung S Voice with Google Voice Search on Your Galaxy S4: http://youtu.be/Gcv88jlyQOs
Skype Trouble Shooting: "Can't open Skype. You are already signed in on this computer..": http://youtu.be/56-vawU-xFQ
Search Any Website Easily with URL Keyword Search for Mozilla FireFox and Google Chrome!: http://youtu.be/XSDHhbnIjhs
Hack into Any Webpage with Any Browser!!!: http://youtu.be/lnwHh5XxR4E
How to fake the amount of YouTube Subscribers with Google Chrome!! ;): http://youtu.be/Jxo23pJApl4 .

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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMhIo5y5Us3eCQS2Fg?e=7xZFj0

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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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiMguq28ziVq8HR6ohw?e=VgPdsp

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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In this video I go over how to easily curve text and other objects with the GIMP Photoshop Program using the Cage Transform option.

Download GIMP for Free: http://www.gimp.org/

Download the GIMP File in my video: https://1drv.ms/u/s!As32ynv0LoaIiMdoWa2yNymg0TfhpA?e=FwIEyL

Related Videos:

GIMP Photoshop Tutorial: http://youtu.be/dSYjD4ov6ao
GIMP Photoshop Tutorial - Adding a Color Border to Text and Objects: http://youtu.be/fTyLewIVB-8
GIMP: Rounding Text Edges with the Gaussian Blurr Function: http://youtu.be/lEAO6Ajr1AY
GIF Animations with GIMP 2.8 - A very simple step-by-step tutorial: http://youtu.be/vg8IFbHsvng
Whiten Teeth with GIMP 2.8 Photoshop - Simple Tutorial: http://youtu.be/2ENln3t6J94 .

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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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Created 3 years, 5 months ago.

800 videos

Category Education

I mainly teach math, but also make "controversial" videos that are censored on YouTube, as well as creating #FreeEnergy technology!