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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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over further into Conic Sections and this time go over the definition of a Hyperbola and derive its resulting formula. I had gone over this derivation several years ago but I have decided to revisit it to be better tie into the Conic Sections video series I have recently been making, as well as to go over it in more detail. The Hyperbola is defined as the set of points on a plane with the property that the difference in the distances from each point to two fixed points (known as the foci) is a constant. Using this definition for the foci on the x-axis, I first show that the difference is equal to +/- 2a because this is the difference when the Hyperbola is also on the x-axis, at either of the two points known as the vertices, and is thus defined as constant for Hyperbolas. The derivation for the hyperbola is very similar to that for the ellipse, which I covered in my earlier video, and involves using the Pythagorean Theorem for the distances and combined with a lot of algebra to simplify the resulting formulation. After some careful algebra, I show that we can eventually write the hyperbola as x^2/a^2 – y^2/b^2 = 1 and where b^2 = c^2 – a^2. The resulting graph of the hyperbola consists of two branches that extend outwards approaching the slant asymptote lines, which I covered in my last two videos, and are y = +/ (b/a)x. This is known as a Horizontal Hyperbola, but we can switch up the x and y terms to get a Vertical Hyperbola y^2/a^2 – x^2/b^2 = 1 and with slant asymptotes y = +/- (a/b)x. This is a very extensive video covering the definition and derivation of Hyperbolas so make sure to watch this video! Video notes: - PDF: https://1drv.ms/b/s!As32ynv0LoaIh5FP9bXo4PFSmGkJZw - HIVE: https://peakd.com/mathematics/@mes/conic-sections-hyperbola-definition-and-formula Related Videos: Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M Slant Asymptote Lines: Example 2: Horizontal Hyperbola: https://youtu.be/XSudAYmWJ-M Slant Asymptote Lines: Example 3: Vertical Hyperbola: https://youtu.be/oFYvWFhcTwI Hyperbola - Definition and derivation of the equation: x^2/a^2 - y^2/b^2 = 1: http://youtu.be/Y6iYC4VEAi0 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a quick review of geometric series and p-series and show the circumstances for when they are convergent. A geometric series has all the terms being a constant number multiplied by a common ratio starting from the power of 0 and incrementing by 1 for each successive term. The series is convergent and equal to the (first term) / (1 - common ratio) when the absolute value of the common ratio is less than 1. I also show a geometric interpretation of the geometric series using similar triangles. A p-series is of the form 1/n^p and it is convergent when p is greater than 1 and divergent for all other values. The timestamps of key parts of the video are listed below: - Question 3: 0:00 - Solution to (a): Geometric series: 0:28 - Geometric representation via similar triangles: 2:04 - Solution to (b): p-Series: 4:51 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I review bounded and monotonic sequences as well as the monotonic sequence theorem. A bounded sequence is one in that is bounded above and bounded below. A sequence is bounded above if there is a number that is less than every term in the sequence. Likewise, a sequence bounded below is if there is a number that is larger than every term in the sequence. A monotonic sequence is either always increasing or always decreasing. The monotonic sequence theorem, which I covered in my earlier video, states that a bounded, monotonic sequence is always convergent. The timestamps of key parts of the video are listed below: - Question 2: 0:00 - Solution to (a): Bounded sequence: 0:22 - Solution to (b): Monotonic sequence: 1:33 - Solution to (c): Monotonic sequence theorem: 2:51 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a quick review of what convergent sequences and convergent series are. A sequence is just a list of numbers, and it is said to be convergent if its limit approaches a specific number as the number of terms gets large. A series is a summation of a sequence, and it is said to be convergent if the limit of the n-th partial sum of the sequence approaches a specific real number. I compare the definitions for when a both the sequence and series converge to the number 3. The timestamps of key parts of the video are listed below: - Question 1: 0:00 - Solution to Part (a): Convergent sequence: 0:39 - Solution to Part (b): Convergent series: 2:29 - Solution to Part (c): Limit of sequence equals 3: 4:31 - Solution to Part (d): Limit of series equals 3: 4:59 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

Join me live as I answer questions regarding 9/11 and debunk the mainstream pancakes and alt-media explosive nonsense; both of which cover up the use of suppressed DEW technology that turned the towers to dust! Related Videos: MES Livestreams: https://www.youtube.com/@mes/streams . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video, Patrick Clawson, a director at an USA-Israel "think tank" in 2012, argues that starting a war with Iran is difficult, so he literally suggests the idea of a covert "crisis initiation" aka false flag to get the USA into a war with Iran. Fast forward to 2023, and the long planned war with Iran is coming. And make no mistake, this will lead to World War 3... Timestamps of key parts of the video: - Final Offer = War with Iran: 0:00 - Iran becoming North Korea = War with Iran: 0:36 - Crisis Initiation = False Flags to start ALL wars: 1:55 - Sanctions and covert attacks against Iran: 3:08 This video is a shortened version of my earlier video listed below: - 2012 Think Tank Lobbyist Patrick Clawson Pushes for 'Crisis Initiation' to Start War with Iran https://youtu.be/4UqrWFUSCnw Related Videos: - Gen. Wesley Clark Reveals Middle East Invasion Was Pre-Planned & Iran is NEXT https://peakd.com/war/@mes/911truth-part-12-gen-wesley-clark-reveals-middle-east-invasion-was-pre-planned-and-iran-is-next . ------------------------------------------------------ Follow MES Truth: Hive: https://peakd.com/@mestruth 3Speak: https://3speak.tv/user/mestruth Odysee: https://odysee.com/@mestruth:9 BitChute: https://www.bitchute.com/profile/95z46OOtOS5o/ Rumble: https://rumble.com/c/c-2016272 DTube: https://d.tube/#!/c/mestruth12 YouTube: https://www.youtube.com/channel/UCmYl-9bhOOotXaNpS-liNiQ MORE links: https://linktr.ee/matheasy MES Links Telegram channel: https://t.me/meslinks Follow Math Easy Solutions: Website: https://MES.fm YouTube: https://youtube.com/@mes Store: https://mes.fm/store Email : contact@mes.fm Donate: https://mes.fm/donate

In this video I derive the formula for projecting 3D coordinates onto a 2D screen using similar triangles. First I plot out the coordinates in 3D and then draw a straight line from the point where we are projecting the coordinates and onto the x = 0 plane. The point of projection can be thought of as the point at which our camera or eyes are located at, thus the resulting 2D projection maintains 3D perspective from that specific point. Drawing a second line passing through the z coordinates of the 3D line, we can see two similar triangles. Either of the similar triangles can be used to obtain identical formulas for the y and z projection coordinates. Note that in this projection derivation, I project the x coordinates to x = 0 and the camera or eyes location is at x = 1000. Epic stuff! The timestamps of key parts of the video are listed below: - Projecting 3D coordinates to 2D coordinates: 0:00 - Two Similar Triangles: 2:45 - Determining the formula for the y and z projection: 4:41 - 3D to 2D projection formula: 8:53 This video was taken from my earlier video listed below: - Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ - HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK Related Videos: Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I project a 3D rectangle onto a 2D screen, while also removing a segment of a line that is behind the rectangle so that it maintains its 3D perspective. I first project the given 3D rectangle coordinates using the 3D to 2D projection equation I derived earlier. Then, I determine the point of intersection of the 3D rectangle and 3D line. The next point that is needed is the point of intersection of the projected 2D line and the bottom portion of the projected 2D rectangle. Once I solve for these, I use GeoGebra to plot the projected line while removing the portion that is behind the rectangle. The resulting 3D chart is truly amazing! https://www.geogebra.org/calculator/twezjbu5 The timestamps of key parts of the video are listed below: - Question 4: Projecting a 3D rectangle to 2D: 0:00 - Solution: Graphing out the rectangle and its projection in GeoGebra: 1:04 - Remove the portion of the line behind the rectangle: 6:12 - Find point of intersection of the 3D line and rectangle: 7:15 - Determining the equation of the plane of the rectangle: 7:47 - Cross product to get the plane normal vector: 15:48 - Calculating the equation of the plane: 21:12 - Plugging in the line equation into the rectangle equation: 27:03 - Graphing the intersection point in GeoGebra: 32:18 - Finding the point of intersection of the projected line and rectangle: 35:03 - Vector equation of bottom right portion of projected rectangle: 38:08 - Equating the projected line equation with the bottom right rectangle line equation: 41:07 - Calculating the point of intersection of projected line and rectangle: 47:10 - Graphing it all out in GeoGebra: 50:30 This video was taken from my earlier video listed below: p - Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ - HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK Related Videos: Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I quickly go over how to verify if our 3D to 2D projection is correct, which I do so by adding sight lines in GeoGebra. These "sight lines" are just lines drawn connecting the coordinates of the camera and the projected points on the screen. If these sight lines intersect our clipped points along the 3D line, then it means our projection is indeed correct. This is because the clipped points are simply projected along a straight line from the camera to the screen. In the amazing GeoGebra 3D graphing calculator, we can quickly create sight lines by using the line segment function: https://www.geogebra.org/calculator/twezjbu5 The timestamps of key parts of the video are listed below: - Question 3: Verifying the Projection with Sight Lines: 0:00 - Solution: 0:18 - Adding sight lines with GeoGebra: 1:31 This video was taken from my earlier video listed below: - Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ - HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK Related Videos: Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I first derive the formula for projecting a 3D point to a 2D screen and then apply that formula to the 3D line from the previous question. To project a 3D image onto a 2D screen, we just have to draw a line extending from the camera or viewpoint that intersects our desired point and extends to the screen. Then applying similar triangles, we can derive the projected coordinates for the y and z coordinates; note that the x-coordinates in this case all get projected to x = 0. Next we apply the derived formula to the clipped 3D line points from Question 1 to obtain the projected coordinates on the 2D screen. And as always, I graph this all out using the amazing GeoGebra 3D graphing calculator: https://www.geogebra.org/calculator/twezjbu5 The timestamps of key parts of the video are listed below: - Question 1: Projecting Clipped 3D Line to 2D: 0:00 - Solution: Deriving 3D to 2D projection equation: 0:12 - Applying similar triangles: 7:18 - Projecting the clipped points of the 3D line: 10:51 - Graphing with GeoGebra: 14:31 This video was taken from my earlier video listed below: - Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ - HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK Related Videos: Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over Question 1 of the Laboratory Project: Putting 3D in Perspective and this time determine the points at which a 3D line needs to be clipped before it is projected onto a 2D screen. To do this, I first obtain the equations of the 4 clipping planes which project from the point of view of the camera or eyes and unto the vertices of the projected screen. Then we can plug in the equation of the 3D line into each linear equation of the planes and obtain points at which the line and planes intersect. Graphing this out in the amazing GeoGebra 3D graphing calculator, it becomes clear that the line only needs to be clipped at the left and top clipping planes. This is an important exercise in the mathematics of projecting 3D images onto 2D screens, which are used throughout computer graphics programming. Here is a link to GeoGebra if you want to play around with the projection: https://www.geogebra.org/calculator/twezjbu5 The timestamps of key parts of the video are listed below: - Laboratory Project: Putting 3D in Perspective: 0:00 - Question 1: Clipping a 3D Line: 2:08 - Solution: Graphing out the question in GeoGebra: 2:38 - We need 4 clipping planes: 4:35 - Recap on the equations of lines and planes: 6:58 - Vector and Parametric Equations of the 3D line: 8:17 - Equation of the right clipping plane: 12:21 - Note on simplified vectors: 21:49 - Linear equation of the right clipping plane: 22:49 - Plugging in equation of a line into the equation of a plane: 24:30 - Plotting our right clipping plane in GeoGebra: 30:49 - Equation of the top clipping plane: 32:47 - Plugging in equation of a line into the equation of a plane: 40:46 - Equation of the left clipping plane: 47:13 - Plugging in L into the plane equation: 50:42 - Equation of the bottom clipping plane: 58:52 - Plugging in L into the plane equation: 1:01:04 - Summary: Line is clipped at left and top clipping planes: 1:03:08 This video was taken from my earlier video listed below: - Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ - HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK Related Videos: Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this MES Truth video I have uploaded a very well done summary of German New Medicine (GNM) by the famous podcaster EyesIsWatchin which he used to help explain what he assumed to have been food poisoning. Steve Eyes, whom also is my cousin, woke up one morning having to vomit and go to the washroom all day. He assumed it was food poisoning but since he had followed the same routine and diet as usual, a subscriber of his pointed out a GNM explanation for this. In this case, Steve Eyes may have been experiencing an "indigestible morsel conflict", which is the conflict of not being able to accept or "digest" a specific event or news. The symptoms he was experiencing are a good sign that the conflict has been resolved and hence the "morsel" is being eliminated. This was during a time when Eyes was having some serious doubts about the direction of his podcasting career and the symptoms occurred a day before his podcast, thus delaying its release. This experience, as well as the constant prodding to research GNM by yours truly MES, helped Steve to understand the importance of GNM and especially the importance of mindset as it relates to health. This video clip was taken from 14:34 to 30:59 mark of the EyesIsWatchin Podcast #102 on June 24, 2023: https://odysee.com/@EyesIsWatchin:f/EyesIsWatchin-Podcast--102:f More resources for learning GNM: - RICHPLANET Show 280: Dr. Ryke Geerd Hamer and the Psychological Link of Cancer: https://youtu.be/Mz_oAnyPxxs - Learning GNM website: https://learninggnm.com/ - The 5 Biological Laws: https://learninggnm.com/SBS/documents/five_laws.html#Second_BL_PCL - Danielle M Bryant https://t.me/gnmukcommunity - Dr. Ryke Geerd Hamer's 2005 presentation: https://peakd.com/hive-128780/@mes/2005-presentation-on-the-5-biological-laws-of-gnm-by-dr-hamer The timestamps of key parts of video are shown below: - German New Medicine explanation for "food poisoning" symptoms: 0:00 - No such thing as a malignant cancer: 6:54 - DICs (Demons in Charge) cover up GNM: 11:23 - Stress is linked to cancer: 13:07 - Cancer cells are natural parts of the body: 14:11 Related Videos: Presentation by Dr. Andrew Kaufman: Humanity is NOT a Virus: https://odysee.com/@mestruth:9/3-Dr.-Andrew-Kaufman-Humanity-is-Not-a-Virus:0 2009 HIV/AIDS Documentary: House of Numbers - Anatomy of an Epidemic: https://youtu.be/lvDqjXTByF4 . ------------------------------------------------------ Follow MES Truth: Hive: https://peakd.com/@mestruth 3Speak: https://3speak.tv/user/mestruth Odysee: https://odysee.com/@mestruth:9 BitChute: https://www.bitchute.com/profile/95z46OOtOS5o/ Rumble: https://rumble.com/c/c-2016272 DTube: https://d.tube/#!/c/mestruth12 YouTube: https://www.youtube.com/channel/UCmYl-9bhOOotXaNpS-liNiQ MORE links: https://linktr.ee/matheasy MES Links Telegram channel: https://t.me/meslinks Follow Math Easy Solutions: Website: https://MES.fm YouTube: https://youtube.com/@mes Store: https://mes.fm/store Email : contact@mes.fm Donate: https://mes.fm/donate

In this video I go over the mathematics involved in computer graphics programming in order to clip and project a 3D image onto a 2D screen while still maintaining 3D perspective. This was taken from my Stewart Calculus book in the Laboratory Project titled Putting 3D in Perspective. Computer graphics programmers have to somehow display 3D images stored in memory onto a 2D screen for users to observe. To do this, the 3D images need to be projected from a point at which the camera or eye is viewing and then onto a 2D screen behind the object, while maintaining perspective. To do this, the equations of 4 clipping planes are first needed to be obtained to clip off the portions of image that will be beyond the projection. In this Project, I derive the clipping plane equations, as well as equations of a 3D line and 3D rectangle, and their their projected formulas. I also go over the concept of "hidden line rendering" to remove objects that are behind other 3D objects, thus saving computing power by not needing to project them onto the screen. And as always, I use the amazing GeoGebra 3D graphing calculator to plot out all the projections, and which you can play around with in this link: https://www.geogebra.org/calculator/twezjbu5 The topics covered as well as their timestamps are listed below. - Introduction: 0:00 - Calculus Book Reference: 1:00 - Sections in Calculus Book Chapter: 1:14 - Topics to Cover: 2:02 - Laboratory Project: Putting 3D in Perspective: 2:54 - 4 Questions: 5:03 - Question 1: 8:10 - Equation of the 3D line: 13:00 - Equation of the Right Clipping Plane: 18:22 - Equation of the Top Clipping Plane: 38:49 - Equation of the Left Clipping Plane: 53:15 - Equation Bottom Clipping Plane: 1:04:55 - Summary: 1:09:10 - Question 2: 1:10:54 - Projecting 3D on to 2D: 1:12:13 - Question 3: 1:27:31 - Question 4: 1:29:39 - Point of Intersection of the Line and Rectangle: 1:36:56 - Point of Intersection of the Projected Line and Projected Rectangle: 2:04:43 - Graphing it All Out in GeoGebra 3D Graphing Calculator: 2:20:10 - Outro: 2:23:31 - PDF video notes: https://1drv.ms/b/s!As32ynv0LoaIirBjY_SU7z2CXBOG1A - HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK - Full Vectors and the Geometry of Space series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ Related Videos: - Vectors and the Geometry of Space: Equations of Lines and Planes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a very unique problem on showing that the n-th partial sum of the harmonic series is NOT an integer. The harmonic series is the sum of the terms 1/i where i is a positive integer. To show that the partial sum is not an integer, we require some truly outside-of-the-box thinking, which fortunately for us is made easier with the given hint. To prove this, we first assume that the partial sum IS an integer and then observe what happens to 2 similar equations. The first is the multiplication of (the product of all odd integers less than or equal to n) * (the largest power of 2 that is less than or equal to n) * (partial sum). The second equation is the same as the first but with the assumption that the partial sum is an integer. After going over some very unique mathematical reasoning, I show that the left side of the equation is always odd while the right side is always even. This is a contradiction and thus the partial sum can not be an integer! Pretty epic brain twister! The timestamps of key parts of the video are listed below: - Problem 26: Partial Sum of Harmonic Series is NOT an Integer: 0:00 - Solution: 2:27 - Right side of hint equation is even: 4:16 - Left side of hint equation is odd: 7:23 - Checking when r is less than k: 13:41 - Checking when r = k: 16:56 - Summary: Partial Sum of Harmonic Series is NOT an integer: 20:45 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I have uploaded an epic edit made by 9/11 Revisionist, which I further corrected, showing a 3D model of the WTC overlaid on top the very tiny rubble pile after the Towers turned to dust in mid-air. The 3D models show the shear scale of the size of the Twin Towers and the rest of the World Trade Center (WTC) complex, which comprised of 7 buildings in total. The WTC was constructed in a shallow slurry wall known as the Bathtub which stretched 70 feet from ground level to the bedrock and was used to protect from the Hudson River. There were 6 floors below ground level. The 3D model shown of the underground floors is not to scale, so I have added a correction in the video. Each Twin Tower was 208 feet wide so the 70 feet to bedrock is relatively very shallow, and much more shallow than depicted in the 3D model. Besides this error, the 3D model does a good job illustrating the construction features and size of the WTC. Later in the video, parts of a presentation by Dr. Judy Wood are shown and voiced over another 3D model of the WTC. This time the 3D model is overlaid ontop of the tiny leftover rubble pile, and clearly demonstrate the astonishing lack of debris and overall disappearance of the Twin Towers. The Twin Towers were made with 110 floors of thick structural steel columns and Dr. Judy Wood correctly points out that their near instant disintegration could not have been done by any conventional gravity collapse or even explosive demolition. The question reiterates throughout the end of the video: Where did the towers go? Original video by 9/11 Revisionist: https://odysee.com/@911revisited:7/Where-did-the-towers-go:4 The timestamps of key parts of the video are listed below: - 3D model of the WTC: 0:00 - Underground Bathtub, NOT TO SCALE: 0:57 - Actual depth of Twin Towers foundation: 1:30 - Cross Section view of the Twin Towers: 1:54 - September 11, 2001: Presentation by Dr. Judy Wood: 2:21 - 3D model of the WTC overlaid above WTC 3: 3:21 - 3D model of the WTC overlaid above the tiny rubble pile: 4:30 - Top view of the WTC tiny rubble pile: 5:02 - Where did the towers go?: 5:43 Related Videos: 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over an interesting math problem which involves differentiating 3 power series to find relationships among them in order to show the given equation is true. In order to differentiate power series, we first need to determine if the series are convergent, which I do so using the Ratio Test. Next we can differentiate the given equation and using our obtained relationships, can show that the equation equals a constant. Plugging in x = 0 into the equation, we can thus simply solve for this constant, and thus prove our given equation. The timestamps of key parts of the video are listed below: - Problem 25: 0:00 - Solution: Using the Ratio Test to determine convergence: 1:33 - Term by Term Differentiation: 8:35 - Differentiating the desired equation: 14:42 - Determining the constant that equals to the desired equation: 20:09 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over an in-depth derivation to determine an explicit formula for the n-th Fibonacci number. The Fibonacci sequence is the sequence of terms where the previous 2 numbers are added together. Prior to making this video, I had not known there was an explicit formula to determine any given number in the Fibonacci sequence. The derivation involves first determining the Maclaurin series for the given function by writing it out as a power series. Doing so yield the coefficients of the Maclaurin series to be just the Fibonacci numbers. The next part of the derivation is to solve for the series of the given function again but this time using a different method, by using partial fractions. This yields two partial fractions that are in the form of the sum of a convergent geometric series. Replacing the partial fractions with their corresponding Geometric series, simplifying the result, and comparing with our prior Maclaurin series, I note that we have in fact an explicit formula for the n-th Fibonacci number. Absolutely amazing and mind-boggling stuff! The timestamps of key parts of the video are listed below: - Problem 24: Series involving Fibonacci series: 0:00 - Solution to (a): The function as a Maclaurin series: 1:37 - Comparing coefficients of powers of x: 7:25 - Each coefficient is equal to the n-th Fibonacci number: 11:27 - Solution to (b): Explicit formula for the n-th Fibonacci number: 13:06 - Completing the square: 13:32 - Writing f(x) as partial fractions: 21:41 - Summary of f(x) as partial fractions: 29:13 - Partial fractions are in the form of the sum of a convergent geometric series: 35:15 - Simplifying the resulting series: 43:52 - Explicit formula for the n-th Fibonacci number: 49:24 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I show that the series whose terms are reciprocals of positive integers, excluding the digit 0, has a sum that is less than 90. This is a very interesting problem as it shows how seemingly arbitrary series can have very simple solutions. To solve this problem, I first group the terms of the series such that each group has the same number of digits in the denominator. Next, I count the number of terms in each grouping and find a general formula for the n-th group. I also note that each term (besides the first one) is less than 1/10^(n-1). From this we can write a formula for the sum of the infinite series, which turns out to be a convergent geometric series. This means we can simply use our formula for the convergent geometric series and obtain our final answer, which is the series is less than 90. Epic stuff! The timestamps of key parts of the video are listed below: - Problem 23: Sum of reciprocals of positive integers without the digit 0: 0:00 - Solution: Group the terms into number of digits: 0:25 - Each term is less than 1/10^(n-1): 5:26 - Max sum of each grouping: 7:18 - Sum of series is less than a convergent geometric series: 9:06 - Sum of series is less than 90: 10:35 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I construct an infinite series of right triangles rotated about a single point and show that the central angle diverges to infinity as the number of triangles approach infinity. To show this, I first construct a table determining the base lengths of each triangle using the Pythagorean Theorem to obtain a formula for the n-th triangle base. From this we can obtain the angle as a formula involving the inverse tangent trigonometric function. Applying the Limit Comparison Test with a diverge p-series, I show, using L'Hospital's Rule, that the angle series diverges, hence the angle approaches infinity as the number of triangles approach infinity. This means that the series of triangles makes infinitely many turns around the central point. The timestamps of key parts of the video are listed below: - Problem 22: Spiraling Triangles: 0:00 - Solution: Repeating Pythagorean Theorem: 1:16 - Formula for n-th Triangle: 5:16 - Limit Comparison Test: 8:57 - Comparing with a Divergent p-series: 10:21 - Applying the Limit Comparison Test with our original series: 14:36 - Recap on tan(x): 18:59 - Applying L'Hospital's Rule: 20:56 - The angle of the triangles diverges to infinity: 22:30 - Recap on the derivative of arctan(x): 23:11 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

This is my first time doing a livestream, so bare with me as I try to figure it out haha I've been getting a lot of comments, messages, and emails asking questions from everything from math questions to 9/11 to Maui (DEW?) fires. It's hard to keep up with all the comments, so I thought I will try livestreaming and answering questions live on air instead. Let me know what you think! Related Videos: MES Livestreams: https://www.youtube.com/@mes/streams . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I find the solutions of an infinite Maclaurin cosine series when it equals to zero. Although we aren't given that the series is a Maclaurin cosine series, we can see this to be the case by looking at our table of common Maclaurin series and replacing the x terms with -x^2. Given the periodic nature of the cosine function, we get an infinite number of solutions as a function of any given integer. I also include an important note at the end of the video about keeping track of the negative signs when transforming functions, something that my Calculus book solutions manual forgot to do! The timestamps of key parts of the video are listed below: - Problem 21: 0:00 - Solution: Case where x ≥ 0 is not a solution: 0:31 - Maclaurin series for cos x : 1:24 - Solutions for cos x = 0: 4:54 - Solutions for f(x) = 0: 7:38 - Note on the Solutions Manual: 9:32 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a pretty amazing infinite series and show, after an extensive math proof, that it equals to ln 2. The series is sum of the infinite terms that follow the pattern 1/(1*2) + 1/(3*4) + 1/(5*6) + ... etc., and somehow this equals to the simple answer of ln 2 or natural log of 2. While the proof is complicated, fortunately the problem has 4 parts to provide the steps to solving for the proof. The steps involve writing a geometric series as an integral and then determining an inequality from solving the definite integral from x = 0 to x = 2 which includes ln 2 in the result. Rearranging the inequality and we obtain our final answer of ln 2. Amazing stuff! The timestamps of key parts of the video are listed below: - Problem 20: 0:00 - Solution to (a): 1:48 - Solution to (b): 6:55 - Solution to (c): 11:54 - Solution to (d): 20:44 - Final answer: Sum of series is ln 2: 25:52 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the sum of an infinite series that can be solved by noting it is just the Maclaurin series for inverse tan for the angle π/6. Using exact trigonometric ratios, by splitting an equilateral triangle and applying the Pythagorean Theorem, I show that tan(π/6) = 1/sqrt(3). This means that the inverse tan or arctan(1/sqrt(3)) = π/6. Plugging this value into our earlier Maclaurin series for tan(x), we obtain a formula that includes are given series in the Problem, which we can solve fairly easily. The timestamps of key parts of the video are listed below: - Problem 19: 0:00 - Solution: Maclaurin series for arctan(x): 0:19 - Exact trig ratios triangle for tan(π/6) 2:45 - Series for arctan(1/sqrt(3)): 5:19 - Alternate form of the solution: 12:40 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 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps