True-False Quiz Question 12: A Divergent Series is Also Absolutely Divergent
In this video I show that a divergent series also means that the absolute value of the series is divergent. This follows from my earlier theorem that an absolutely convergent series is also convergent. Thus if the opposite were true, a divergent series would mean that it would be absolutely convergent, and hence convergent, which is a contradiction! Thus, the answer to the question is True, and a divergent series is also absolutely divergent.
Note that I made a typo in the video, the absolute value sign should be inside the summation series. Nonetheless, I solved it as if was inside.
Time stamps:
- Question 12: 0:00 - Solution: True: 0:13 - Theorem: An absolutely convergent series is also convergent: 1:44
In this video I go over an example on determining the distance between two parallel planes. The first step is to find a point on one of the planes and then next is to simply apply the distance formula between a point to a plane that I derived in my earlier video. I also double check the distance by calculating it using the amazing GeoGebra 3D graphing calculator, which you can play around with here: https://www.geogebra.org/calculator/zmwhau8b
The timestamps of key parts of the video are listed below:
- Example 9: Distance Between Parallel Planes: 0:00
- Applying the Distance Formula from a Point to a Plane: 1:57
- Calculating Distance with GeoGebra 3D Graphing Calculator: 6:35
This video was taken from my earlier video listed below:
- Equations of Lines and Planes: https://youtu.be/qWQz6qPhXR8
- Video notes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FO3u0IupqllNNkZTsffpIV
Related videos:
Vectors and the Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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In #MESExperiments 20 I’ve uploaded one of the least known experiments by the late great Eric Laithwaite and it is among the clearest demonstrations of gyroscopic weight loss through forced precession. This experiment involves placing a gyro wheel with a shaft that is loosely connected onto a vertical rod which allows the gyro and shaft setup to freely move upwards if the gyro “chooses” to. And choosing to rise upwards is exactly what it does as Eric forces the precession with an external looped structure which he pushes against the end of the shaft.
As the gyro torques upwards and thus the center of mass increases so too does the entire gyro + shaft setup rise; and in fact rise completely airborne for a brief moment. Thus, had there been a weight scale underneath, it would measure a zero weight reading as it was airborne; in other words, the gyro “loses weight” during forced precession, or more accurately, as the center of mass increases and without expected downwards reaction (which otherwise would increase the weight scale reading akin to a person pushing off the ground when jumping upwards).
This experiment is taken from the BBC “Heretics” series referenced below. Interestingly it is not available on YouTube, and BBC doesn’t allow anyone to upload it there either; thus raising the question of why the tax payer funded BBC, to the tune of about $5+ billion per year, places a cover on science. In fact even the video itself is a coverup of true gyro physics as it intermixes Eric's (conventional) physics defying experiments with nonsense commentary from the narrator and fake "scientists" that serve to merely confuse the public.
- Banned YouTube Video: https://www.youtube.com/watch?v=dy6hLZ02naM
Luckily I found an upload on Dailymotion and have also added a local video download link in case it gets removed there too.
- Dailymotion “Heretics” Video: http://www.dailymotion.com/video/x2ya0y4
- Local Download Link: https://1drv.ms/v/s!As32ynv0LoaIh5sxvfDT9KkkVF1Hog
Interestingly, this simple and clear-cut demonstration of gyroscopic weight loss is something that controlled fake science outlets such as the Veritasium YouTube channel (along with the BBC and Wikipedia et al) would rather have covered up; and which I explain in further detail in my world changing #AntiGravity Part 6 video: https://peakd.com/antigravity/@mes/antigravity-part-6-video-1-objects-in-rotation-defy-mainstream-physics-mes-duality-concept.
Also, I would briefly like to mention that, as explained in #MESScience 1: https://peakd.com/messcience/@mes/messcience-1-how-does-a-powerball-gyroscope-work-gyros-are-inverted-pendulums, that precession is always forced, hence a gyroscope when merely rising on its own like in many of my earlier experiments should also be losing weight as the center of mass rises. But in those cases the rate of rising is often too slow for most weight scales to detect.
The full experiment results can be viewed on Hive: https://peakd.com/mesexperiments/@mes/mesexperiments-20-forced-precession-of-a-gyroscope-generates-inertial-lift-i-e-weight-loss.
Stay Tuned for #MESExperiments 21…
Related Videos:
?#MESScience 1: How Does a Powerball Gyroscope Work? + Gyros Are Inverted Pendulums: https://peakd.com/messcience/@mes/messcience-1-how-does-a-powerball-gyroscope-work-gyros-are-inverted-pendulums
☝#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
#MESExperiments Video Series: https://peakd.com/mesexperiments/@mes/list
DRAFT #MESExperiments Video Series: https://mes.fm/experiments-draft
#MESScience Video Series: https://peakd.com/science/@mes/tutorials
#AntiGravity Video Series: https://peakd.com/antigravity/@mes/series
#FreeEnergy Video Series: https://mes.fm/freeenergy-playlist .
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Ever wonder how Rainbows are formed and why the colors follow the order they do? Well calculus can help and in this video I show using differential calculus just how sun rays are scattered in rain drops and why we see rainbows in an ordered color scheme.
View calculations on webpage: http://www.trishock.com/academic/rainbows.shtml
Download the notes in my video:
- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIiboBb8gX7SAjOp_TYw?e=DONRV3
- Excel notes: https://1drv.ms/x/s!As32ynv0LoaIibl75ItOSDIWqibQqA?e=MHla5V
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/applied-project-how-rainbows-are-formed
Related Videos:
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw
Angles - Degrees vs Radians: What are Radians??: http://youtu.be/bOdrVvQWRdE
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Implicit Differentiation - A Brief Introduction: http://youtu.be/12OY1b3DYHQ
Derivative of Trigonometry Functions: Derivative of sin(x): http://youtu.be/elEvQ4Wu7Pk
Derivative Rules: Proof of Chain Rule: http://youtu.be/tYDDpKzP-VU
Derivative Examples using the Chain Rule: http://youtu.be/KB9_lBxTrwI .
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In this video I have uploaded and dubbed over with my voice the background information section of the 11 hour documentary that I had uploaded earlier. That documentary, titled 9/11 Observable Evidence, was made by anonymous authors and included many quiet text parts. Thus, I have decided to dub over the entire documentary as well as split it into smaller clips to make it more easily digestible. The authors state they made the documentary as a tribute to Dr. Judy Wood and Andrew Johnson, whom have both been instrumental to bringing the real truth of 9/11 to the public spotlight. The links to their websites are listed below:
- Dr. Judy Wood's website: http://drjudywood.com
- Buy the book: Where Did the Towers Go?: https://wheredidthetowersgo.com/
- Andrew Johnson's website: https://checktheevidence.com
- Read the book: 9/11 Finding the Truth: https://tinyurl.com/911ftb
- Anonymous authors' correspondence with Andrew Johnson: https://www.checktheevidence.com/wordpress/2021/12/27/9-11-liars-for-truth-what-happened-on-9-11-and-how-it-was-covered-up/
The timestamps of key parts of the video are listed below:
- 9/11 Observable Evidence Documentary Intro: 0:00
- MES Note: Dubbing Over With My Voice: 0:19
- Background Information: 0:39
- Links to Dr. Judy Wood and Andrew Johnson Books: 3:01
- Documentary Table of Contents: 3:50
This video was taken from the following video listed below:
- 9/11 Observable Evidence (MES Dubbed): Still Working On It...
- 9/11 Observable Evidence (Original): https://youtu.be/8Xw-00NbEE8
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_HHWt33moIqEeUBP3cgCh
Related Videos:
- #911Truth video series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EzqTamtIXtgX8QudQSxuxh and https://peakd.com/truth/@mes/911 .
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https://www.youtube.com/watch?v=sFgHaBNPNL4
In this video I go over the results section of the main paper on COVID-19 "virus" isolation and look at the first part which is on the patients used in the paper. Three adult patients with severe pneumonia (inflammation of the lungs) were admitted in a Wuhan hospital in December 2019. Patients 1 and 3 survived but Patient 2 died after being put on a mechanical ventilator (it is not clear if the other patients were also put on a mechanical ventilator or not). No biopsy or tissue samples were obtained from any of the samples. CT scans were provided for Patient 2 and showed cloudy regions termed "bilateral fluffy opacities". Personally, there was nothing significant with these 3 patients, besides possibly the use of mechanical ventilation in making the patients pneumonia worse...
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: Patients: 0:00
- Tomography, Computed Tomography (CT) Scan, Radiography: 1:22
- Patient 2 Received Mechanical Ventilation and Died: 3:03
- Respiratory Distress, Ventilator, Biopsy: 3:42
- Chest Radiographs: 4:23
- Trachea, Intubation, Bilateral Fluffy Opacities: 5:48
- Summary of Patients Results: 7:43
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=FdK7d7iB2TE
In this video I go over a quick recap on how the sum of a series affects the limit of its terms and its partial sums. If an infinite series sums up to 3, then this must mean that the terms of the series all approach the limit of 0 while the limit of the partial sums approach 3. In other words, the limit of the sequence of partial sums is equal to the sum of the infinite series.
The timestamps of key parts of the video are listed below:
- Question 4: 0:00
- Solution: 0:47
- Limits of the sequence vs partial sums: 1:06
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=10SkjrJBqbs
In this video I go over another example on trig substitution for integrals and solve the integral of the function 1/sqrt(x^2 - a^2). In this example I use the trig substitution x = a*sec(θ).
Download the notes in my video: http://1drv.ms/1PyB5xi
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometric-substitution-for-integrals-example-5
Related Videos:
Trigonometric Substitution for Integrals: One to One Function: http://youtu.be/QO26MkCC3eU
Trigonometric Substitution for Integrals: Example 4: http://youtu.be/v3tHdU63Vio
Trigonometric Substitution for Integrals: Example 3: http://youtu.be/Tfl90TqW3jA
The Area of an Ellipse (and Circle): http://youtu.be/7hSkKPQA71s
Trigonometric Substitution for Integrals: Example 1: http://youtu.be/lpp6YLWB2GM
Trigonometric Substitution for Integrals: http://youtu.be/2pWvGXwtVJo
Inverse Functions Part 2: One to One Functions and the Horizontal Line Test: http://youtu.be/iSNuplUWrbA
Trigonometry: Derivative of sec(x): Proof: http://youtu.be/0sO0TehqMOw
Hyperbolic Trigonometry Identity Proof: 1-tanh^2(x) = sech^2(x): http://youtu.be/yM_JBV0P8hM
Trigonometric Identity: Integral of sec(x): http://youtu.be/s-AyOdd9kuc .
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https://www.youtube.com/watch?v=X-35GgXPEHQ
In this video I go over the vector equation of a line segment instead of the entire line. I first start off with an example involving parametric equations and noting that setting the parameter t = 0 gets the first point on the line, while setting it to t = 1 gets the second point. From this fact, we can start off with our usual vector equation of a line and then describe it using our desired starting and ending vector, which point to the 2 positions of a line we want. Then we can just impose the interval of the parameter t to be from 0 to 1 to get our desired line segment!
The timestamps of key parts of the video are listed below:
- Parametric Equations of a Line Segment Example: 0:00
- General Vector Equation of a Line Segment: 5:32
- Summary of Equation of a Line Segment: 11:58
- Note on t = 0 and t = 1: 12:40
This video was taken from my earlier video listed below:
- Equations of Lines and Planes: https://youtu.be/qWQz6qPhXR8
- Video notes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FO3u0IupqllNNkZTsffpIV
Related videos:
Vectors and the Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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https://www.youtube.com/watch?v=WG8C-5aonjY
In this video I go over the same “cow grazing area” problem in which a cow (or goat or other farmyard animal) is tied to a circular silo and we are asked to determine the total area in which the cow can graze around. But this time I go over another method in solving this problem, Method 2, and show break the area under the involute curve of the circle into infinite sectors of a circle, which we can sum up as an integral. This method is actually much easier than in the parametric equations used in Method 1, and saves plenty of time too. This integration method is based on the area formula that I derived in my earlier video for the area of a polar curve. The only difference is that instead of having a direct formula for the involute curve, we can simply project the angle of a sector of a circle perpendicularly towards the involute because we know the length of the rope. This is actually an ingenious method in solving the grazing area problem and shows that complex problems can be solved easily with a thorough understanding of mathematics. The difference in the amount of work required in both Method 1 and Method 2 also show how certain techniques are better suited than others in certain situations, which illustrates the remarkable flexibility of calculus, so make sure to watch both methods!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvV-EUB2O3mB0v8-SA
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-area-example-3-cow-grazing-area-method-2
Related Videos:
Parametric Calculus: Areas: Example 2: Cow Grazing Area: Method 1: https://youtu.be/pYf_c_CK5kE
Polar Coordinates: Area Formula: https://youtu.be/wd-EwiKzqa0
Polar Coordinates: Area: Example 1: r = cos 2ϴ: https://youtu.be/6kavQyGcODo
Polar Coordinates: Area: Example 2: Cardioid and Circle: https://youtu.be/vSzxzNn3EiA
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Area of a Sector of a Circle: Proof: https://youtu.be/lglnySF8DyY
Angles - Degrees vs Radians: What are Radians??: http://youtu.be/bOdrVvQWRdE
Parametric Calculus: Example 1: Involute of a Circle: https://youtu.be/NIGw_dlEzQ4 .
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https://www.youtube.com/watch?v=oyoLlcVZWVE