Limits - Examples Part 2 - One Sided Limits Approach
In this video I go further into exploring examples on limits where you can not simply solve them right away but require to break them up into separate functions and apply the one-sided-limit approach in solving them. Basically for functions that are 2 in one such as absolute value type functions, you need to first find the limit by approaching the x-value from the left and from the right sides of it and the limit exists if and only if you approach the same limit from both sides. These are very useful examples so make sure to watch!
In #MESExperiments 28 I demonstrate the amazing ability of the GyroTop magnetic spinning top to always balance opposite the magnetic attractive force even when turning the apparatus upside down. The GyroTop, also called Space Top, is the invention of an obscure person named Owen Liang, and whom created it to test his hypothesis that spinning tops want to align themselves opposite of gravity rather than simply "maintaining angular momentum".
The first part of the video involves just a regular spinning top with the ring magnet removed, and is used as a comparison. The spinning top keeps upright opposite the force of gravity even when the apparatus is tilted. This demonstration is often used to illustrate "angular momentum".
In the second part of the video, I attach the ring magnet and repeat the same procedure of spinning it up with a drill. Note the GyroTop has a tube to manually blow air into to spin it up, but I used my drill instead. As I rotate the apparatus the GyroTop always moves to align against the magnetic attraction. This is counterintuitive since the angular momentum should keep the top stationary until the magnetic attractive force is strong enough to grab hold of the top. This GyroTop opens up lots of possibilities!
Further information, screenshots, and relevant links are included on the Hive blockchain: https://peakd.com/hive-128780/@mes/mesexperiments-28-magnetic-spinning-top-aligns-opposite-of-magnetic-attraction
The timestamps of the regular vs magnetic spinning tops are shown below:
- Regular Spinning Top: 0:00
- Magnetic Spinning Top: 0:59
Stay tuned for #MESExperiments 29...
Related Videos:
#MESExperiments video series: https://peakd.com/experiments/@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
?#MESExperiments 27: Spin Friction Can Make Gyroscope Rise from Steep 70° Angle (No Casing Rotation)
?#MESExperiments 25: Increasing Spin Friction Can Make Gyroscopes Rise Much Faster: https://peakd.com/hive-128780/@mes/mesexperiments-25-increasing-spin-friction-can-make-gyroscopes-rise-much-faster
?#MESExperiments 13: Steepest Gyroscope Rising Experiment Ever! 74 Degrees from the Vertical: https://peakd.com/mesexperiments/@mes/mesexperiments-13-steepest-gyroscope-rising-experiment-ever-74-degrees-from-the-vertical-magic
?#MESExperiments 3: Gyroscopes Exert 'Inertial Forces' With ZERO Loss of Spin Rate: https://peakd.com/mesexperiments/@mes/mesexperiments-3-gyroscopes-exert-inertial-forces-with-zero-loss-of-spin-rate-freeenergy
?#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://ecency.com/antigravity/@mes/antigravity-part-6-video-1-objects-in-rotation-defy-mainstream-physics-mes-duality-concept .
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https://www.youtube.com/watch?v=vOW2EX1rQSo
In this video I go over another example on Parametric Curves and this time look at the manually sketching the shape formed by the parametric equations: x = cos(t) and y = sin(2t). The shape formed is known as the Lissajous figure and has a unique and iconic shape. I sketch the figure by first graphing x = cost(t) and y = sin(2t) separately but by aligning them horizontally and vertically so that the x and y axes align to the axes of the Lissajous figure. From this alignment we can then begin to plot x and y points at each value of t. Although the shape that I manually draw isn't the neatest, I show how to generate this curve using an online parametric equation graphing calculator. While it is good to use online tools to plot the points it is still important to know how to generate these curves by hand because it requires the underlying understanding of the nature of these parametric curves. This is a great video on manually graphing parametric equations so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIht9M4Jk82lFfHjyYDg
View Video Notes on Steemit: https://steemit.com/steemstem/@mes/parametric-curves-example-5-lissajous-figure
Related Videos:
Parametric Curves: Example 4: https://youtu.be/WZYIS1My-g4
Parametric Curves: Example 3: https://youtu.be/VpiJdEviBbk
Parametric Curves: Example 2: https://youtu.be/SBkzZDlqTTE
Parametric Curves: Example 1: https://youtu.be/0k7QyWa9-HA
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8 .
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https://www.youtube.com/watch?v=0OT1OnnAQ9I
In this video I go over some extra more random coincidences involving Donald Trump's June 14th birthday. These set of coincidences are not as related to Trump as the previous 10 main ones I covered earlier but nonetheless they are very interesting, so I have decided to cover them briefly. These extra coincidences are listed below alongside their corresponding video timestamps:
- Most Watched NBA Game was on June 14, 1998: 0:00
- Michael Jordan Game 6 Buzzer Beater and 666 Numerology: 2:12
- June 14, 1994 Vancouver Canucks Stanley Cup Riot After Losing Game 7 to New York Rangers: 2:56
- June 15, 2011 Vancouver Canucks Stanley Cup Riot After Losing Another Game 7 to Boston Bruins: 4:07
- First Mass Transport to Auschwitz Concentration Camp on June 14, 1940: 4:53
- First Mass Deportation by the Soviet Union in Occupied Territories on June 14, 1941: 5:46
- European Space Research Organization Founded on June 14, 1964: 6:53
- Ukrainian Air Force Plane Shot Down by Russian Separatists on June 14, 2014: 7:53
- June 14, 2019: Ukraine Blames Russian Army for Plane Shootdown
- Comedian Heather McDonald was Born on June 14, 1970: 10:01
- Controlled Opposition Group International Center for 9/11 Justice Launches on June 12, 2023: 11:55
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=1GsTnIEsUaM
In this video, I go over a corollary to the previous video in which I determined the cross product length as equaling |a| |b| sin θ. The corollary or theorem that follows from the cross product length is that if the vectors a and b are parallel, then the angle between them are either 0 or 180 degrees or π radians. Thus, the sine term vanishes and becomes 0; and so does the cross product! This means that we can determine if any 2 vectors are parallel if and only if their cross product is equal to 0.
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: The Cross Product: https://youtu.be/k8GRt95i-Gc
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FuRJ8rg-YVQvfPoPOwhuRW
Related Videos:
Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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https://www.youtube.com/watch?v=MyJB7qNsBWo
In this video I go over yet another example on trig substitution for integrals and this time solve the integral of the function x/sqrt(3-2x-x^2). In this example we first have to rewrite the function inside the square root by completing the square and using regular substitution to make it in the form we are familiar with to apply trig substitution.
Download the notes in my video: http://1drv.ms/1IPOOxY
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometric-substitution-for-integrals-example-7
Related Videos:
Trigonometric Substitution for Integrals: Example 6: http://youtu.be/wh2dlrFbxrQ
Trigonometric Substitution for Integrals: Example 5: http://youtu.be/X-35GgXPEHQ
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
Completing the Square: http://youtu.be/5uxV6-f_qc0
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY .
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https://www.youtube.com/watch?v=YtxDMBbsDUM
In this video I go over part B of Question 3 of the Applied Project: Calculus and Baseball. In part A I looked at the time it takes for an outfielder to field a ball and throw it directly to the catcher at home plate. In part B however, I look at whether it is faster or slower for the outfielder to throw the ball to the shortstop instead, and then have him throw it to catcher, assuming that the shortstop can throw faster than the outfielder. As this video will show, the time depends on how fast the shortstop can throw. In the example of the shortstop throwing at 105 ft/s, a direct throw is faster, but at 115 ft/s it is better to relay the ball to the shortstop first.
This is a very extensive and detailed video on analyzing both where the shortstop should be relative to the home plate to minimize the time it takes for the ball to get to the catcher, as well as determining at various speeds if it is better to relay or throw directly to the catcher. In minimizing the time, the first derivative test was also utilized. This may be a long video but it is definitely worth watching to understand just how complex the mathematics are behind even the most basic aspects of baseball. But since often times the difference between an out or a run is just fractions of a second, it is important for baseball managers to utilize mathematics in helping get any competitive edge they can!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtNyM2SqGpX5RBT8dg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applied-project-calculus-of-baseball-question-3b
Related Videos:
Applied Project: Calculus of Baseball: Question 3A: https://youtu.be/9D6WDz_M6AM
Applied Project: Calculus of Baseball: Question 2: https://youtu.be/1iaw0PT4hX4
Applied Project: Calculus of Baseball: Question 1: https://youtu.be/qxSoinW3fKY
Applied Project: Calculus of Baseball: Question 1: https://youtu.be/qxSoinW3fKY
Applied Project: How Fast Does a Tank Drain? Question 1: https://youtu.be/KhsbeI9QPls
Applied Project: How Rainbows are Formed and the Order of it's Colors : http://youtu.be/Q3Euh4K93_c
Applied Project: How Double Rainbows are formed - Calculus of Rainbows Part 2 : http://youtu.be/bKfyV_YKLR4
Applied Project: The Shape of a Can - The Science behind Can Manufacturing : http://youtu.be/pfpd8RJi9jw
Applied Project: Where Should a Pilot Start Descent?: http://youtu.be/DI4WMqrYB4Q
Applied Project: Building a Better Roller Coaster: http://youtu.be/QjtaMIlKYxQ
Applied Project: Where to Sit at the Movies: http://youtu.be/oEkFJuCE-4A
Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI
Derivative of y = Log(x) and y = Ln(x): http://youtu.be/5e6MisvvMPE
First Derivative Test: http://youtu.be/9W4ejz0EMtE
Addition and Subtraction by Hand - An
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https://www.youtube.com/watch?v=nmQYeJr75-k
In this video I go over the geometric interpretation of the length of a cross product and show that it is indeed the area of the parallelogram formed by the two vectors a and b. I first illustrate this geometric view and then do 2 examples on it. In the first example I find a vector perpendicular to a plane spanned by 3 points, and in the second example I determine the area of this plane. Since there are 3 points, the area is just a triangle and is equal to half the parallelogram formed from the cross product length of the perpendicular vector from the first example.
The timestamps of key parts of the video are listed below:
- Geometric Characterization of Theorem 2: 0:00
- Example 3: 4:27
- Example 4: 16:24
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: The Cross Product: https://youtu.be/k8GRt95i-Gc
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FuRJ8rg-YVQvfPoPOwhuRW
Related Videos:
Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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https://www.youtube.com/watch?v=Y_B36uIHwOQ
In this video I go over the law of sines in its most common and basic form and prove it using the equation for the area of a triangle but by writing the area of a triangle in 3 different ways using the 3 different sides of the triangle as a base. The formula for the law of sines or sine law is: sinA/a = sinB/b = sinC/c. The more advanced version of the law of sines simply states that the law of sines also equals the diameter of the circumcircle of the triangle. The circumcircle is the circle that can be drawn that has all 3 points of the triangle touching the circle. I will go over this in a later video so stay tuned!
Download the notes in my video: http://1drv.ms/1MYMd49
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/law-of-sines-basic-proof
Related Videos:
Proof that Sum of Angles in ANY Triangle = 180 degrees: http://youtu.be/4bI3BXIe2k8
Area of a Triangle - A simple proof that A = b*h/2: http://youtu.be/wUT_KN5pshQ
Area of a Triangle Proof - Part 2: When the base is NOT the longest side of the triangle: http://youtu.be/xTVP-HHBP0U
Trigonometry: Proof of Law of Cosines (and Pythagorean Theorem): http://youtu.be/wOCYb3Ku6yw .
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https://www.youtube.com/watch?v=_HDM60RRh8U
In this video I go over the remarkable and puzzling story of Stephen Newman rescuing 9/11 burn victim Kenneth Summers, whom was completely burned from head to toe with all of his skin coming off from his forearms and face, and his hair was all gone, but somehow none of his clothes were burned! This is a baffling witness testimony that has been largely ignored by both mainstream and alt-media channels, besides a few disinfo channels focusing on the part about an "explosion". As with all things 9/11, the events that took place that day involved advanced highly classified directed energy technology capable of turning entire buildings and even people into dust. This witness testimony show cases that Kenneth (Ken) Summers was affected by a non-conventional phenomenon, capable of burning his skin but keeping his clothes in tact. Listening to Ken closely, it appears he was also also "thrown out" of the building, but which he states "next thing I know I was lying out in the middle of the driveway". This appears to be another case of levitation, which was also experienced by many others on 9/11. Furthermore, Stephen Newman said that another surreal thing he witnessed was of the thousands of people he saw on the morning of 9/11, there was not a single victim besides Ken. The full extent of what actually happened on 9/11 requires a lifetime quest to explore, and explore I shall!
Original videos and MSM articles about the story:
- September 29, 2007 video: Stephen Newman ABC interview on September 12, 2001: https://youtu.be/R6iIELNRkBY
- July 17, 2011 video: Kenneth Summers NBC interview: https://youtu.be/1IPT548KzT8
- May 23, 2017 video: Kenneth Summers TIME interview: https://youtu.be/naOsHONFd8Q
- September 9, 2016 TIME article about the video: Survivors of Terror Attacks on How They Moved Forward: ‘You Live Anyway’: https://time.com/4484248/911-september-11-anniversary-terror-attack-survivors/
- September 6, 2011 article by CBS: 9/11 Burn Victim Recounts Story Of His Rescue By Stranger: https://www.cbsnews.com/newyork/news/911-burn-victim-recounts-story-of-his-rescue-by-stranger/
- October 14, 2001 article by New York Times: Trade Center Burn Victim's Long Road: https://archive.ph/x2RP0
The timestamps of key parts of the video are listed below:
- Stephen Newman ABC interview: https://youtu.be/R6iIELNRkBY: 0:00
- Stephen sees Kenneth Summers severly burned: 1:17
- "Fireball" threw Ken back onto the street: 1:42
- But none of Ken's clothes were burned: 2:12
- Stephen took Ken across the Hudson River to a New Jersey hospital: 2:27
- Stephen saw thousands of people but no victims besides Ken!: 3:38
- "Ken was his name": 4:12
- South Tower fell while they were in New Jersey: 4:41
- Kenneth Summers NBC interview: https://youtu.be/1IPT548KzT8: 5:27
- Ken hears a "whooshing, roaring noise": 5:56
- Ken says he heard a "boom and the ground tremble": 6:18
- Revolving door and Lobby filled with a "yellowish brownish combustible mixture": 6:37
- "Major explosion" throws Ken out of the revolving door and onto outside: 7:03
- Ken was on fire but quickly puts out his shirt fire and hair: 7:18
- Kenneth Summers TIME interview + burns marks on his hand: https://youtu.be/naOsHONFd8Q 7:29
- Ken hears a "thud" as he was leaving the WTC 1 lobby: 7:39
- Revolving door temperature got as hot as an oven: 8:13
- "Next thing I know I was lying out in the middle of the driveway..." 8:20
- Stephen Newman testimony voice over Kenneth Summers' burn picture: 8:31
Related videos:
- 9/11 Observable Evidence video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_HHWt33moIqEeUBP3cgCh
- #911Truth video series: 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=c6zN0-FH7ks