In this video I go over further into infinite sequences and series and this time go over the end-of-chapter Problems Plus section of advanced math questions. There are a total of 27 questions in this section: 1 example + 26 problems. These problems are more advanced than the typical questions in my calculus book and are a great way to test how well you know the concepts covered. Try to solve them yourself before watching the solution!
The topics covered in this video are listed below with their time stamps.
- Introduction - 0:00 - Problems Plus - 1:23 - Topics to Cover - 1:54 - Example - 2:29 - Problem 1 - 16:53 - Problem 2 - 23:58 - Problem 3 - 35:27 - Problem 4 - 1:05:21 - Problem 5 - 1:31:38 - Problem 6 - 2:03:57 - Problem 7 - 2:14:25 - Problem 8- 3:16:19 - Problem 9 - 3:44:25 - Problem 10 - 4:05:47 - Problem 11 - 4:21:35 - Problem 12 - 4:35:12 - Problem 13 - 4:56:02 - Problem 14 - 5:26:33 - Problem 15 - 5:38:41 - Problem 16 - 6:00:57 - Problem 17 - 6:16:06 - Problem 18 - 6:54:16 - Problem 19 - 7:23:42 - Problem 20 - 7:37:31 - Problem 21 - 8:04:29 - Problem 22 - 8:15:36 - Problem 23 - 8:39:05 - Problem 24 - 8:51:03 - Problem 25 - 9:43:11 - Problem 26 - 10:05:10
In this video I go over the bizarre occult rituals by NASA pioneer Jack Parsons and Scientologist L. Ron Hubbard in their attempts to produce a magical being called the Moonchild, and which may somehow be none other than Donald J. Trump... According to the infamous occultist Aleister Crowley's Thelma religion, the Moonchild or Moon Child is a magical being produced from impregnating a woman by the goddess Babalon in order to help or save humanity. Parsons and Hubbard undertook a series of rituals, called Babalon Working, from January to March 1946 in hopes of producing this being. While no child was said to be born, nonetheless Parsons said it was a success, and even writing that the spirit of Babalon is on the Earth just before his untimely death.
The Babalon Working rituals are bizarre enough, the timing of specific events somehow raise the question as to whether the Moonchild may in fact be Donald Trump. Firstly, Aleister Crowley wrote a letter to his student Grady Louis McMurtry criticizing Jack and Ron for their attempts at producing this Moonchild; and this letter just so happens to be on the Blood Moon birthday of Donald Trump on June 14, 1946. Fast forward to 2018, after which Trump is now President, and a TV Series is released about the life of Jack Parsons called Strange Angel. This TV series was released on June 14, 2018 and the first scene of the entire series was a Blood Moon! Truly fascinating stuff!
Lastly, this wasn't included in the video, but apparently at the end of the last episode in Season 2 of Strange Angel, L. Ron Hubbard was introduced setting the stage for Season 3 and likely the Babalon Working rituals, but Season 3 was never produced. Time will tell if they bring it back if (or when) Trump becomes President again...
The timestamps of key parts of the video are listed below:
- Coincidence 3: Aleister Crowley's June 14, 1946 Letter about the Moonchild: 0:00
- Background on the Moonchild: 3:44
- Jack Parsons, Ron Hubbard, and the Babalon Working: 6 :45
- Jack Parson Moon Crater: 8:47
- Ron Hubbard, and Scientologists Voting for Trump: 9:02
- Coincidence 4: Strange Angel TV Series Released on June 14, 2018: 11:29
- Jack Parsons: Jet Propelled Antichrist Documentary: 14:22
This video was taken from my earlier video listed below:
- ? Strange Coincidences Involving Donald Trump's Birthday: https://youtu.be/Yd0Ah2Komco
- HIVE video notes: https://peakd.com/hive-106474/@mes/coincidences-involving-donald-trumps-birthday
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElXMhiVmHKyq9IiI0SFYBk
Related Videos:
Full MES Occult video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EX_SJASwVeZMA-CMgu6-Ox .
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https://www.youtube.com/watch?v=fG9Xy5Z6fSw
In this video I go over an example on graphing a circle and a cylinder in 3D coordinates. The circle that I graph has the equation x^2 + y^2 = 1 and z = 3. This means that the circle is centered about the xy-axis origin but at a height of z = 3. The cylinder that I graph just has the equation x^2 + y^2 = 1. In the context of 3D coordinates this means it is a vertical cylinder with an indefinite height. Note that in the context of 2D coordinates, this would just be a circle centered about the xy-axis origin.
The timestamps of key parts of the video are listed below:
- Example 2a: Circle: 0:00
- Example 2b: Cylinder: 2:05
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: 3D Coordinate Systems: https://youtu.be/xJ-qPJFf2gE
- Video notes: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GiAJeLMzhOsrMliibfce5m
Related videos:
Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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https://www.youtube.com/watch?v=JfCmic70QmA
In this video I go over an example on using calculus to find the tangents to parametric curves. This example has multiple parts to it, and in this video I solve Part 1 which involves determining the equations of multiple tangents lines at one specific point on a parametric curve. This is possible for parametric curves because multiple values of the parameter can give the same x and y coordinates. This is one of the cool features of parametric equations which allows some very amazing graphs to be drawn up. In later parts of this example, I will show how to use calculus to manually draw the rest of this parametric curve, so stay tuned!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuI3KTgNgJLTtUF9WA
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-tangents-example-1-part-1
Related Videos:
Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Equation of a Line - A Simple Explanation: http://youtu.be/a3ntO-xNN5M .
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https://www.youtube.com/watch?v=QBD_TvcJuTo
What better way to begin my #MESExperiments video series than by demonstrating one of the most universally unknown properties of gyroscopes: their ability to RISE UPWARDS as they precess. In this experiment I show that this ability of gyroscopes depends partially on the angle it is tilted relative to the vertical but depends mainly on the amount of “friction” of the surface it is placed on. The lower the friction, the better the gyroscope’s ability to magically rise.
Even when it precesses about a rotating platform, the gyroscope can still rise upwards! The rotating platform is a good way to minimize the friction between the gyroscope stem and the surface it is placed on. What’s also VERY interesting, is that with higher friction, the gyroscope may even lower to the ground in a matter of seconds; while with lower friction the gyroscope precesses for several minutes longer upwards, and, as I will show in my later experiments, it remains upright for a much longer time than higher friction surfaces.
This is a truly amazing demonstration of just another magical property of gyroscopes. Let me know what you think is going on here! Note that the precession speed increases presumably as the gyro wheel spin speed decreases, thus providing an acceleration in precession speed. An acceleration, in mainstream science terms, indicates a “force” or “torque”. Is this self-created “force” the reason behind why it is rising? Well if you stay tuned for my later experiments, especially my #AntiGravity Part 6 video, it is almost certainly an intrinsic property of matter to INTERACT with gravity through rotational motion. #StayTuned
Anyways, let me know what you think and stay tuned for my next experiment!
View video notes on the Hive blockchain: https://peakd.com/mesexperiments/@mes/mesexperiments-1-gyroscopes-precess-upwards-on-low-friction-and-rotating-surfaces
Related Videos:
#MESExperiments video series: https://peakd.com/mesexperiments/@mes/list
DRAFT #MESExperiments Video Series: https://mes.fm/experiments-draft
#MESScience video series: https://mes.fm/science-playlist
#AntiGravity video series: https://peakd.com/antigravity/@mes/series
#FreeEnergy video series: https://mes.fm/freeenergy-playlist .
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In this video I recap on Taylor polynomials, Taylor series, Maclaurin series, and Taylor's inequality. A Taylor polynomial is a finite sum with terms consisting of the i-th derivative at a divided by the i-th factorial and multiplied by (x - a) to the power of i. A Taylor series is just an infinite Taylor polynomial. A Maclaurin series is a special type of Taylor series where a = 0. A function is equal to its Taylor series if the remainder approaches 0 as n approaches infinity. Taylor's Inequality states that if the (n + 1) derivative of f(x) is less than or equal to a number M then the absolute value of the n-th remainder of a Taylor series is less than M divided by (n + 1) factorial multiplied by the absolute value of (x - a) to the power of (n + 1). Taylor and Maclaurin series are very useful since they can turn complicated functions into a simple sum of many easily calculatable terms, and is how most calculators work behind the scenes!
The timestamps of key parts of the video are listed below:
- Question 10: 0:00
- (a) Taylor polynomial: 0:42
- (b) Taylor series: 2:20
- (c) Maclaurin series: 3:33
- (d) A function equals its Taylor series if the remainder approaches 0: 4:26
- (e) Taylor's Inequality: 5:45
This video was taken from my earlier video listed 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:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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https://www.youtube.com/watch?v=EHzM_93T1IY
In #MESExperiments 31 I have uploaded a video by the late Francis McCabe demonstrating that a group of randomly orientated gyroscopes will automatically align themselves in the direction of an applied torque. McCabe constructed a machine with 4 gyro horizons from World War 2 (WW2) planes fixed to an assembly that is free to rotate manually via a crank. A gyro horizon is an instrument used to measure an aircraft's orientation relative to the Earth's horizon. When McCabe starts the machine, the gyroscopes are spun up with air pressure and start oscillating and/or rotating (which McCabe describes as "motorization"). He notes that their is a self-developed frequency of oscillation and motorization. Then he applies an external torque by rotating the crank and immediately all the gyroscope line up! He notes that the force is felt only initially as the gyros are lining up and then the machines starts "coasting".
This machine demonstrates what may well be the first mechanical rendition of inertia, which is a mass' resistance to change or acceleration. The gyros can be considered as tiny atoms, and the inertia that an object possesses is related to how many atoms need to reorient themselves in the direction of applied motion. Interestingly, this gyro assembly is also a good illustration of magnetism, since an externally applied magnetic field causes many tiny magnets to reorient themselves in the applied magnetic field direction. Are atoms and magnets just tiny gyroscopes? gyroscopes of the Aether? I think so!
Francis McCabe was an inventor and rocket scientist that had stumbled upon the work of the late great Eric Laithwaite regarding gyroscopes. His original video and his now deleted Wikipedia page are listed below:
- Original video: https://youtu.be/vP4emXJ_GS0
- Archive of Francis Joseph McCabe's deleted Wikipedia page: https://archive.fo/dbwIx
- Gyro horizon or Attitude indicator Wiki: https://en.wikipedia.org/wiki/Attitude_indicator
The timestamps of key moments of the experiment are listed below.
- Assembly of 4 gyro horizons: 0:00
- Starting up the machine: 0:33
- Random positioning of spinning gyroscopes: 1:40
- Applying an external torque by turning the crank: 2:09
- Gyros line themselves to applied torque: 2:18
- Period of inertia is over once gyros line up: 2:44
- Feeling a force only during the gyro lining up period: 2:55
Stay tuned for #MESExperiments 31...
View experiment screenshots and more experiments below:
- Screenshots of the Experiment: https://peakd.com/hive-128780/@mes/eysvgejq
- #MESExperiments video series: https://peakd.com/mesexperiments/@mes/list
- DRAFT #MESExperiments video series: https://mes.fm/experiments-draft
Related Videos:
#MESScience video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0GhjCHmTw1XbqMD_EdVKdd9
#AntiGravity video series: https://peakd.com/antigravity/@mes/series
#FreeEnergy video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FKVpHL_onhaqBeVP-8qJXV
- ?#MESExperiments 8: Large Gyro Wheel Precesses at 1000X Torque Over-Unity https://youtu.be/6q0qXRetpB4
- ?#MESExperiments 20: Forced Precession of a Gyroscope Generates Inertial Lift (i.e. Weight Loss): https://youtu.be/xTrwlo8B3rs
- ☝#AntiGravity Part 6: Objects in Rotation Defy ‘Mainstream’ Physics + MES Duality Concept: https://peakd.com/antigravity/@mes/antigravity-part-6-video-1-objects-in-rotation-defy-mainstream-physics-mes-duality-concept .
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In this video I go over another example on Slant Asymptotes and this time look at the slant asymptote lines of a horizontal hyperbola, which is a hyperbola that extends outwards horizontally. The hyperbola x^2/a^2 – y^2/b^2 = 1 where a and b are constants has slant asymptote lines y = +/- (b/a)x. This is proven by applying the definition of slant asymptotes which I covered in my earlier video, and that is the limit as x approaches infinity of the difference between the function and a line approaches zero. In other words the function, in this case the hyperbola, approaches the asymptote lines. In proving this, I first rearrange the hyperbola to write it as y = f(x). But since the function involves square rooting a square, we get a two part function that can be either positive or negative, and thus to save time I combined all of the +/- terms (as well as the limit as x approaches +/- infinity) in just one limit formula. This was a shortcut on my part, but nonetheless the result is the same for this particular example as compared with doing it individually. I will be referencing this example on slant asymptotes for a horizontal hyperbola in my later videos, so make sure you watch this video and understand the derivation!
- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh5E1eR_74BRIMsvEmA
- Hive notes: https://peakd.com/mathematics/@mes/slant-asymptote-lines-example-2-horizontal-hyperbola
- Limits playlist: https://www.youtube.com/playlist?list=PLFE39AF0D7E0651AC
Related Videos:
Slant Asymptote Lines: Example 1: Rational Function: https://youtu.be/FT5yNtPeBvg
Slant Asymptote Lines + Special Case: Rational Functions and Long Division: https://youtu.be/QX2nfi5JtQs
Hyperbola - Definition and derivation of the equation: x^2/a^2 - y^2/b^2 = 1: http://youtu.be/Y6iYC4VEAi0
Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI .
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In this video I go over the main COVID-19 "virus" isolation paper and look at the results section titled "Detection and Isolation of a Novel Coronavirus". While the title of the section suggests a "new virus" was discovered, the actual methodology used to come to this conclusion is lacking, to say the least. The usual virology methodology was used, which was take RNA from a handful of patients, assume it's from a "virus", and then use genetic sequencing technology to somehow obtain 20,000 short RNA sequences and compare with known "viral sequences" in an online database. Then PCR tests were performed with high cycle threshold values to detect common sequences shared among a group of "beta-coronaviruses". Growing cell cultures on human airway cells, monkey kidney cells, and liver cancer cells were assumed to be the same as "isolating" the "virus". The cell cultures were then observed for "cytopathic effects" and compared with a "mock infected" cell culture (with no detail given of this "mock infected" culture), and the images provided of the cytopathic effects were unclear, and insignificant in my opinion. Finally, the electron micrographs were provided of the heavily processed cell cultures and cell culture supernatants, supposedly showing the "virus" particles along with their "solar corona" spikes. Again, to me this is not strong evidence of "viruses", nor even of what exactly these particles are or what they do or can do, if anything.
The paper is listed below:
- A Novel Coronavirus from Patients with Pneumonia in China, 2019
- Authors: Na Zhu et al
- Published on January 24, 2020 in The New England Journal of Medicine (NEJM)
- https://www.nejm.org/doi/full/10.1056/NEJMoa2001017
The timestamps of key parts of the video are listed below:
- Paper Results: Detection and Isolation of a "Novel Coronavirus": 0:00
- HCoVs, RNA Template to Clone, Viral Reads: 2:46
- PCR to Detect Known "Viral RNA Regions": 3:40
- PCR Cycle Threshold (Ct), VERO Cell Lines, Cloning Cell Lines: 4:35
- Cytopathic Effects of "Infected" and Mock-Infected Cell Cultures: 9:20
- Mock-Infected, Cilium Beating: 10:47
- Electron Micrographs of Alleged "Virus" Particles: 11:17
- Pleomorphism, Solar Corona, Extracellular "Virus" Particles, "Virus" Inclusion Bodies: 13:49
- Summary of "New Virus" Detection and Isolation: 16:36
This video is taken from my earlier video listed below:
- ?#MESScience 4: Review of COVID-19 "Virus" Isolation Paper: https://youtu.be/cvDO85Rw4d8
- Video notes: https://peakd.com/hive-128780/@mes/messcience-4-review-of-covid-19-virus-isolation-paper
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0E4aQ_cq4ZDD2WGiDU5vVgx
Related Videos:
?#MESScience: MES Science Tutorials: https://mes.fm/science-playlist .
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https://www.youtube.com/watch?v=d0wUJSdQe5s
A simple proof of the very important and useful trigonometry Identity sin^2(x) + cos^2(x) = 1 is shown. Also the notation for squaring trigonometric functions is shown. Since the proof requires the use of the Pythagorean theorem, this identity is called the Pythagorean trigonometric identity.
Video Notes:
- PDF: https://1drv.ms/b/s!As32ynv0LoaIitRdSUPZcae4SrtYHg
- HIVE: https://peakd.com/hive-128780/@mes/trigonometry-identity-proof-that-sin2x-cos2x-1
Related Videos:
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y) : http://youtu.be/VuQczhk7HOs
Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x): http://youtu.be/EynSefQs308
Trigonometry Identities: sin(x +/- y) = sin(x)cos(y) +/- cos(x)sin(y): http://youtu.be/edtk9thfwbM .
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