In this video I go over further into improper integrals and this time discuss the type 1, Infinite Intervals, in great detail as well as outlining a definition for it. The first type of improper integrals is when the interval is infinite, such as the integral of a function from x = a to infinity. Even though the interval may be infinite the actual integral may approach a finite number if the limit of the function at positive or negative infinity exists.
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!
Download the notes in my video: https://www.dropbox.com/s/xyx8hazvw1m1pvw/270%20-%20Limit%20Laws%20Part%202%20-%20History.pdf
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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https://www.youtube.com/watch?v=K5n7y2BvnOs
In this video I go over a seemingly complicated infinite limit and solve it by first considering a special simpler case. I show the simpler case is true and then follow the same steps to show the general case is also true. This type of problem solving technique is called "Using Analogy" and is very useful at getting a starting point when looking at problems that appear complicated. For example, if a question involves large numbers, we can start off by solving it for smaller numbers and hopefully it will give clues as to how to solve it for bigger numbers.
The timestamps of key parts of the video are listed below:
- Problem 10: 0:00
- Solution: Using an analogy: 0:56
- Special cases, k = 1 and k = 2: 2:15
- General case: 8:10
- Limit is equal to 0: 14:26
This video was taken from my earlier video listed below:
- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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Time to get back to my life goal of creating a free energy device, and the first one I hope to replicate and validate is Bruce DePalma's N-machine, which is essentially a magnetized gyroscope.
Related Videos:
- MES Livestreams: https://www.youtube.com/@mes/streams
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FqwyUa_ICwTlqO0S6Y3kAn .
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In this video I go over a two-part problem that involves proving a trigonometric identity and then using that identity to find the sum of an infinite series. The trig identity involves a half angle tangent function. The infinite series involves solving with a telescoping sum and applying L'Hospital's Rule.
The timestamps of key parts of the video are listed below:
- Problem 3: 0:00
- Solution to (a): Prove the Trig Identity: 0:34
- Solution to (b): Sum of Series: 5:19
- Telescoping Sum: 11:39
- Applying L'Hospital's Rule: 21:29
- Putting it All Together: 24:30
This video was taken from my earlier video listed below:
- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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https://www.youtube.com/watch?v=hHXvaZge0GA
In this video I show that the number 0.99999.... can be written as a convergent geometric series whose sum is equal to 1. The number 0.99999... can be written as 0.9 + 0.09 + 0.009 + ... which can further be written as 0.9 + 0.9(0.1) + 0.9(0.1)^2 + ... which is just a geometric series. In our case, r = 0.1 and is less than 1, thus the geometric series is convergent and we can apply the formula for the sum, which is just 1. Thus the answer to the question is True: 0.99999 ... = 1. Fascinating stuff!
Time stamps:
- Question 19: 0:00
- Solution: True: Geometric Series 0:14
- Sum of a Convergent Geometric Series 3:04
- Sum of Geometric Series = 1: 5:00
Full video below:
- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L
Related Videos:
Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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In #FreeEnergy Part 1 I introduce my newest video research series which I hope to uncover suppressed Free Energy technology in hopes of deriving the mathematics behind it and eventually create my own device, all made publicly availability for everyone to replicate it! This video series stems from my ongoing #911Truth video series (https://mes.fm/911truth-playlist) which explores the brilliant work of Dr. Judy Wood and her book “Where Did the Towers Go?” (Buy it here! https://mes.fm/judywoodbook). The most important aspect of 9/11 was “who” was behind it but rather “what” actually happened, which was the towers turned to dust in mid-air using advanced hidden directed free energy technology! This is a fact, and this very fact is the motivation and driving force behind my #FreeEnergy video series in unlocking the technology and science hidden from us!
In Part 1, I go over an overview of the mainstream view on suppressed technology and science to illustrate how anything and everything against conventional science is swift to the side and discredited. From the work of Roger Anderton that contends that science was “steered” in the wrong direction through errors in Albert Einstein’s work to Rupert Sheldrake and Graham Hancock being censored for giving TED talks questioning dogmatic belief-based assertions by mainstream science such as Fundamental Constants actually being constant or that Consciousness needs to be scientifically explored. If these scientific dogmas such as the speed of light being constant was not actually constant, then this would mean we need to re-investigate Quantum Mechanics and Special Relativity, and may need to start anew in the time of Roger Boscovich whom may have already been on his way to deriving the “Unifying Theory of Everything”. For the hardline skeptics, keep in mind that even famous π is actually “wrong” and should have been replaced with τ = 2π a long time ago. In fact I may start using τ because I am starting to realize that this confusion may actually have been by design...
I also go over the mainstream Wikipedia view on #FreeEnergy only to see the typical underreporting, complete censorship of Dr. Judy Wood, and the usual discrediting of unconventional science researchers as “conspiracy theorists”. What’s most interesting is the work of Stanley Pons and Martin Fleischmann in 1989 which claimed to have created “Cold Fusion” or nuclear reactions at room temperature, just by a simple table-top experiment! Now instead of the United States allocating funding to them, all funding was removed, and an active smear and discredit campaign was launched to shut down Pons and Fleischmann’s work. Other researchers such as Eugene Mallove and Stanley Meyer were VERY suspiciously killed whil
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https://www.youtube.com/watch?v=0odnMzawafE
In this video I go over a brief introduction on the most commonly used probability density function, the normal distribution. This function is represented by a bell-shaped curve, often referred to as the Bell Curve, and models many natural phenomena well, such as test scores, rainfall, heights, weights, etc. Although I go over the basics of the normal distribution function and its properties in terms of the standard deviation, I leave the actual derivation of the formula to later videos, as it is more advanced. So stay tuned for those videos!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsBSj6EePdgyR-ZAAg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/probability-normal-distribution
Related Videos:
Probability: Median: Example 1: https://youtu.be/nDAfJfCa4Fc
Probability: Median: https://youtu.be/C8ZU8BjHIqQ
Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value (or Mean Value): https://youtu.be/gF-zRmdTUWw
Probability: Example 2: Exponentially Decreasing Probability Density Function: https://youtu.be/QeU_9NDCXoA
Probability: Example 1: https://youtu.be/SDJPja8GJ1Q
Probability: Introduction: https://youtu.be/H_sfVMH0VpQ
Probability that my friend Dmitry Scores Goals: http://youtu.be/zbAN04Kj3D8
Three Prisoners Problem: http://youtu.be/8vY66MD7nsM
Odds of Having a Perfect NCAA March Madness Bracket: http://youtu.be/It1sCq9cAFM
Odds of Winning the Lottery: http://youtu.be/dVNFhu6tMQc
Blood Flow: Poiseuille's Law: https://youtu.be/X6aU0p7wJzI
Applications of Integrals: Hydrostatic Pressure and Force: https://youtu.be/fesMt6vmXIo
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Moments and Centers of Mass: Constant Density: https://youtu.be/3bglr1sRWUc .
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...
https://www.youtube.com/watch?v=b17gJ4F_v54
In this video I have uploaded NASA's RS-25 space shuttle engine test which quite literally creates giant clouds! The test is from October 19, 2017 and took place at NASA's Stennis Space Center in Mississippi, USA. The RS-25 engine is produced by the American company Aerojet Rocketdyne and is a liquid-fuel cryogenic rocket engine. The engine burns liquid hydrogen and liquid oxygen, which together form H20 or water, and hence the giant clouds of water vapor being exhausted outwards into the sky. The RS-25 is the latest engine being developed by NASA with hopes of using it in the new Artemis Moon missions program as well as possibly for future Mars missions.
Note that I have sped up the majority of the video by 10X speed to better grasp just how much water vapor is being exhausted outwards.
#RS25 #NASA #Artemis #clouds #Moon
The original video as well as links to more information on the RS-25 and Artemis are shown below:
- Original video: NASA Tests 2nd RS-25 Flight Engine for Space Launch System: https://images.nasa.gov/details/SSC_2017-10-19%20-%20RS-25%20Test and https://youtu.be/lFqfCDEp6iw
- RS-25 engine Wikipedia: https://en.wikipedia.org/wiki/RS-25
- How the RS-25 works: https://archive.ph/wip/4UWWP
- NASA Artemis Moon missions: https://www.nasa.gov/specials/artemis/
- Artemis program Wikipedia: https://en.wikipedia.org/wiki/Artemis_program
- April 5, 2023 RS-25 test: https://images.nasa.gov/details/SSC_2023-04-05_RS-25_Engine_Test and https://youtu.be/I4ldyG9NSeU
- Top Gear films NASA engine tests on October 29, 2010: https://youtu.be/BIpeNs5OWbo .
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...
https://www.youtube.com/watch?v=C9vfoBiBI2k
In this video I go over some laws of logarithms and prove the law ln(x*y) = ln(x) + ln(y). In my earlier videos on logs and their properties I proved this same law but using the definition of logarithms as the inverse of the exponential function. In this video, however, I show how to prove logarithm laws using integrals and derivatives like I explained in my last video.
Download the notes in my video: http://1drv.ms/1lSyj6A
Related Videos:
Natural Logarithmns Defined as Integrals: Introduction: http://youtu.be/M-N2PQ5UZns
Inverse Functions - f-1(x) - An Introduction: http://youtu.be/qIqj3oKwFi8
Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI
Natural Logarithms, Log base 10, and Some Examples Using Logs: http://youtu.be/XRSkMk5L3pk
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk .
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...
https://www.youtube.com/watch?v=2SCZzFy2b2s