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Chain Rule for Derivatives Examples: Part 4
In this video I go over some more useful examples on the chain rule for derivatives and look at functions within functions within functions and thus require using the chain rule multiple times.
Download the notes in my video: https://www.dropbox.com/s/uqlpxfn5gyxeq59/414%20-%20Chain%20Rule%20Examples%20Part%204.pdf
Related Videos:
Chain Rule Examples: Part 1: http://youtu.be/j1YKstIMIFc
Chain Rule Examples: Part 2: http://youtu.be/kX6ourBH9KE
Chain Rule Derivatives: Examples Part 3: http://youtu.be/J769tWFpy70
Derivative Rules: Proof of Chain Rule: http://youtu.be/tYDDpKzP-VU
Derivative Examples using the Chain Rule: http://youtu.be/KB9_lBxTrwI
Derivative of Trigonometry Functions: Derivative of sin(x): http://youtu.be/elEvQ4Wu7Pk
Derivative of Trigonometry Functions: Derivative of cos(x): http://youtu.be/LMjVp-GsrCw
Derivative of Trigonometry Functions: Derivative of tan(x): http://youtu.be/Jf6p4crjrSc
Trigonometry: Derivative of sec(x): Proof: http://youtu.be/0sO0TehqMOw
The Number e - A Brief Introduction and it's Derivative: http://youtu.be/o_s_YYD6v3g .
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https://www.youtube.com/watch?v=3neWNOz1Wf8
Download the notes in my video: https://www.dropbox.com/s/uqlpxfn5gyxeq59/414%20-%20Chain%20Rule%20Examples%20Part%204.pdf
Related Videos:
Chain Rule Examples: Part 1: http://youtu.be/j1YKstIMIFc
Chain Rule Examples: Part 2: http://youtu.be/kX6ourBH9KE
Chain Rule Derivatives: Examples Part 3: http://youtu.be/J769tWFpy70
Derivative Rules: Proof of Chain Rule: http://youtu.be/tYDDpKzP-VU
Derivative Examples using the Chain Rule: http://youtu.be/KB9_lBxTrwI
Derivative of Trigonometry Functions: Derivative of sin(x): http://youtu.be/elEvQ4Wu7Pk
Derivative of Trigonometry Functions: Derivative of cos(x): http://youtu.be/LMjVp-GsrCw
Derivative of Trigonometry Functions: Derivative of tan(x): http://youtu.be/Jf6p4crjrSc
Trigonometry: Derivative of sec(x): Proof: http://youtu.be/0sO0TehqMOw
The Number e - A Brief Introduction and it's Derivative: http://youtu.be/o_s_YYD6v3g .
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COINC
Coincidences-3-and-4-Donald-Trump-Moonchild
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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LAWS
laws-of-logarithms-ln-x-y-ln-x-ln-y
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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POLAR
polar-coordinates-example-6-part-1
In this video I go over another example on polar coordinates, and in this example I sketch the polar equation r = 2cosθ. This is the first part of a two part example question, the second which I will do in a later video is on converting this polar equation to Cartesian form. In this first part, I sketch this curve by finding several coordinates which have angles that we know the exact trigonometric ratios for. Graphing several of this points onto a polar coordinate system, the shape appears to be a circle (which indeed is). Also, I explain how if extend past the domain of the angle between 0 to pi, we simply just plot the same points again. Also for angles that are in the 2nd or third quadrant, I show that we end up getting a negative r value, and thus we move the distance backwards to, again, get the same points onto the circle. This is a really important example in understanding how to manually sketch polar equations, especially those involving trigonometry, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhulaAxdqyyJRly7wJg
#HIVE video notes: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-example-6-part-1-sketching-a-circle
Related Videos:
Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A
Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs
Polar Coordinates: Example 3: Cartesian to Polar: https://youtu.be/mV-9KTQM-RU
Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE
Polar Coordinates: https://youtu.be/-KAdZL-N4ok
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Exact Trigonometry Ratios: Amazing Memory Trick: http://youtu.be/78Em2CW0Sf4
Proof that Sum of Angles in ANY Triangle = 180 degrees: http://youtu.be/4bI3BXIe2k8
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8 .
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FIRST
first-derivative-test-example-y-x-2sin-x
In this video I go over an example on finding the local maximum and minimum of a function using the first derivative test. The example I go over is the function y = x + 2sin(x).
Download the notes in my video: http://1drv.ms/1mOsJCl
Related Videos:
Increasing/Decreasing Test for Derivatives: Proof: http://youtu.be/b6kpWalTHrk
Increasing/Decreasing Test Example: http://youtu.be/6-J_6GPhLZE
First Derivative Test: http://youtu.be/9W4ejz0EMtE
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY
Trigonometry Graphing: Sin, Cos, Tan Functions: http://youtu.be/l_3cgeq-YXE
Local and Absolute Max/Min and Critical Points/Numbers: http://youtu.be/aOvwQaEFbjw
Derivative of Trigonometry Functions: Derivative of sin(x): http://youtu.be/elEvQ4Wu7Pk .
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EXPON
Exponential-Functions-and-Graphing
Exponential Functions are introduced in this tutorial and the different types of graphs that they comprise are also shown.
- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIitIxaYOmJKMlrj2pkg
- HIVE notes: https://peakd.com/hive-128780/@mes/exponential-functions-and-graphing
Related Videos:
Exponential Functions - Example on Radioactive Decay and Half-Life: http://youtu.be/dmMRX82zqlc
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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?#MES
mesexperiments-6-gyroscopes-precess-with
In #MESExperiments number 6, I repeat my 5th experiment of a precessing gyroscope on ice but this time set the gyroscope at a near horizontal angle. And yet again the gyroscope demonstrates the (mainstream) physics-defying ability to magically precess with ZERO centripetal force, at sufficient gyro spin rate. In other words, the gyroscope precess as if it magically lost all its “mass” and thus generating ZERO “horizontal force” at the stem; and as explained in Experiment number 4, the gyroscope literally precesses without “angular momentum”. This is some truly mind-boggling properties of gyroscopes which, if viewed with the critical eye, requires a re-writing of centuries old (mainstream) physics textbooks and even science in general.
Once the gyroscope loses spin speed, the “centripetal force” gradually increases which can be seen by the stem of the gyroscope moving in a circular direction on the near frictionless ice surface. But even at these slower spin speeds, the amount of “centripetal force” is almost negligible. This is because, as shown in my earlier experiments, it just takes an incredibly small amount of “friction” to hold the gyroscope in place. And in fact it is this gyroscope’s magical property of seemingly behave “massless” that allows it to precess perfectly balanced even on the tip of your finger.
I can’t stress how monumental and game-changing these HIDDEN-IN-PLAIN-SITE properties of gyroscopes, because after all a gyroscope is essentially a constrained spinning top, and which a spinning top itself is just matter in rotation… Which begs the questions what is “matter” and why does rotation magically change its properties?
Stay Tuned for #MESExperiments Number 7!
View full experiment results on the Hive blockchain: https://peakd.com/mesexperiments/@mes/mesexperiments-6-gyroscopes-precess-with-zero-centripetal-force-on-ice-even-at-horizontal-angle
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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REVIE
review-question-7-estimating-sums-for
In this video I recap on estimating the sum of a series based on whether it converges by the Integral Test, Comparison Test, or the Alternating Series Tests. If a series is convergent by the Integral Test, we can estimate its sum by first finding an estimate of the size of its remainder. Since an integral is formed by an infinite set of rectangles, the remainder can be estimated based on whether the rectangles are above or below the curve. From this, we can estimate the sum of the series for the integral test.
If a series is convergent by the Comparison Test, we can estimate its sum by estimating the sum of the series it is being compared to. For example, if a series is less than another series that happens to converge by the integral test, we can use the sum estimate for the integral test.
If a series is convergent by the alternating series test, we can apply the alternating series estimation theorem. This theorem states that the absolute value of the remainder of the n-th partial sum of a series is less than the next positive term of the series. This can be seen visually since each subsequent term is larger than the difference between the sum and any given partial sum.
The timestamps of key parts of the video are listed below:
- Question 7: 0:00
- (a) Integral Test sum estimation: 0:27
- Estimating the size of the remainder: 1:47
- Remainder estimate for the integral test: 6:57
- (b) Estimating sum using the Comparison Test: 8:25
- (c) Estimating sum of alternating series: 15:02
- Visualization of the alternating series estimation theorem: 16:31
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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APPLI
applications-of-integrals-surface-area-2
In this video I go over another example on determining the area of a surface obtained by rotating a curve about an axis. In this example, I calculate the surface area of a shape formed by rotating the arc of the parabola y = x^2 from the point (1, 1) to (2, 4) about the y-axis. As a check of the answer obtained, I calculate the shape of a cylinder as well as a frustum of a cone that is similar to the shape we are trying to calculate, thus the resulting surface areas should all be similar as well.
The solution I use in this video uses the surface area formula in which the arc length is written using dx as opposed to dy. In my next video I solve this same example using dy in the arc length formula instead so stay tuned for that video!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103605&authkey=!AMWD5-Q4RS1QsQo&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-surface-area-example-2-solution-1
Related Videos:
Applications of Integrals: Surface Area: Example 1: https://youtu.be/E9rwIVUifuA
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8 .
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DIFFE
differential-equations-example-2-initial
In this video I go over another example on differential equations and this time discuss the more practical need for finding a particular solution to a differential equation as opposed to a general solution. One such solution involves satisfying the additional requirement that the solution has a specific initial value. Thus in solving such a problem, known as an initial value problem, we get one particular solution. In this example I look back at the same differential equation from Example 1 but this time apply the initial condition y(0) = 2.
Thus in the physical sense, the particular solution to an initial value problem means that we take our initial known or measured condition and then predict the future values from this starting point. This is a pretty interesting video on how to go about solving an initial value problem so make sure to watch this video!
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Related Videos:
Differential Equations: Example 1: https://youtu.be/n575RKO48Ro
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .
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