Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-ab/ab

Why we study differential calculus. Created by Sal Khan.

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AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

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Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/sc....ience/ap-chemistry-b

The electrons in an atom are arranged in shells that surround the nucleus, with each successive shell being farther from the nucleus. Electron shells consist of one or more subshells, and subshells consist of one or more atomic orbitals. Electrons in the same subshell have the same energy, while electrons in different shells or subshells have different energies. View more lessons or practice this subject at https://www.khanacademy.org/sc....ience/ap-chemistry-b

Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc

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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-calculus-bc/bc


The ratio test is a most useful test for series convergence. It caries over intuition from geometric series to more general series. Learn more about it here.

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channe....l/UC5A2DBjjUVNz8axD-
Subscribe to Khan Academy: https://www.youtube.com/subscr....iption_center?add_us

Learn about key details and more reading comprehension lessons in the FREE Khan Academy Kids app! https://go.learn.khanacademy.o....rg/khanacademy/YouTu

In this video, Reya and Sandy ask questions while they read a story. They wonder about what happens and pay attention to details along the way.

Visit us at http://www.khankids.org to learn more about Khan Academy Kids, a free educational app for preschool through 2nd grade available on Apple, Google Play, and Amazon app stores.

You can also access other videos on our Reading Comprehension playlist here: http://khan.co/KhanKids-ReadingComprehension.

Subscribe to our channel for more videos like this.

Questions? Reach our team at khankids@khanacademy.org.

Learn more counting, addition, and subtraction lessons in the FREE Khan Academy Kids app! https://go.learn.khanacademy.o....rg/khanacademy/YouTu

Peck learns subtraction by counting backward with strawberries. Way to count on, Peck!

Visit us at http://www.khankids.org to learn more about Khan Academy Kids, a free educational app for preschool through 2nd grade available on Apple, Google Play, and Amazon app stores.

You can also access other videos on our Addition and Subtraction playlist here: http://khan.co/KhanKids-AdditionSubtraction

Subscribe to our channel for more videos like this.

Questions? Reach our team at khankids@khanacademy.org.

2nd Channel: https://www.youtube.com/channe....l/UCPdc6bs3I8s6Y4QE_
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Created by Daniel Turner (B.A. (Hons) in History, University College London)

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There would always be men who would have a special bond with their personal weapons. Sometimes it was so great that they preferred using their own guns from home instead of the army-issued ones in combat.

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Credit:
Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Dejan Milivojevic
Narrator:

Bryan 'Lazlo' Beauregard

Though we often think of the Vikings of Scandinavia as being barbarians, when it came to warfare they were quite advanced warriors, as well as being highly practical. So they tended to favour weapons that served a purpose in everyday life, as well as on the battlefield.

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Credit:
Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Conan White
Narrator:

Bryan 'Lazlo' Beauregard

Music Credit
Crusade - Video Classica by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/

Source: http://incompetech.com/music/r....oyalty-free/index.ht

Artist: http://incompetech.com/

Sources:

Weapons of the Viking Warrior
By Gareth Williams

The Viking Age: The Early History, Manners, and Customs of the ..., Volume 2
By Paul Belloni Du Chaillu

Ancient Weapons in Britain
By Logan Thompson

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Food Rations from the 19th century to the present day.
Meal, Ready-to-Eat
The modern ration has been refined over many years and various conflicts to be both nutritionally balanced and contain all the calories a soldier requires when in the field, with one MRE bag containing approximately 1250 calories. In addition to this, the MRE has been designed to fulfil all operational requirements. This means that they remain shelf stable for a minimum of three years, or nine months in warmer climates. They also are highly durable and have the ability to survive non-parachute drops of 100 feet and parachute drops of 1250 feet. With all these elements considered, a soldier can eat a full, nutritional meal wherever they find themselves.

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Credit:
Created by Daniel Turner (B.A. (Hons) in History, University College London)

Narrator:

Chris Kane
https://vocalforge.com/

Where did Vladimir Putin come from? What was Putin’s education? Who pushed Putin to pursue a meteoric rise to Prime Minister and President of the largest country in the word? Watch Putin’s history unfold from his modest origins to the dominant figure he is today.

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Credit:
Created by Daniel Turner (B.A. (Hons) in History, University College London)



Narrator:
Bryan 'Lazlo' Beauregard


Sources:


· Sebestyen, Victor (2018), Lenin the Dictator
· Truscott, Peter (2005). Putin's Progress: A Biography of Russia's Enigmatic President, Vladimir Putin
· Lynch, Allen. Vladimir Putin and Russian Statecraft
· Vladimir Putin; Nataliya Gevorkyan; Natalya Timakova; Andrei Kolesnikov (2000). First Person: An Astonishingly Frank Self-Portrait by Russia's President Vladimir Putin
· Rosefielde, Steven; Hedlund, Stefan (2009). Russia Since 1980
· Dawisha, Karen (2015). Putin's Kleptocracy: Who Owns Russia?

Play World of Warships here: https://wo.ws/3aaFBpX
Thank you World of Warships for sponsoring this video.
During registration use the code FIRE to get for free: 200 doubloons, 1 million credits, the Premium Battleship Tier 5 - USS Texas, 20x Restless Fire Camouflage, and 7 Days Premium Account.

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Credit:
Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Dejan Milivojevic
Narrator:

Chris Kane
https://vocalforge.com/

Sources:
Cole, Roger, and Richard Belfield. SAS Operation Storm. Hodder & Stoughton, 2011.
White, Rowland. Storm Front. Corgi, 2012.
“Battle of Mirbat: The near Alamo of the Special Air Service.” SOFREP, 5 Mar. 2020, sofrep.com/news/special-air-services-secret-war-oman-part-5/
Malcher, Author Alan. “The Battle of Mirbat, Oman, 19 July 1972: 22nd Special Air Service Regiment.” Alan Malcher, 15 Dec. 2021,

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One of the most iconic visual elements of the Second World War are German panzers blitzing their way across enemy territory, leaving a trail of death and destruction in their wake.
During the First World War, German tanks had a less than auspicious start. Their first attempt at a tank design was the A7V, a clunky metal box on tracks, a far cry from the formidable vehicles of a quarter century later.



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Credit:
Show Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Robert de Graaf
Narrator:

Chris Kane
https://vocalforge.com/

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Land reform, where estates had been taken from rich landowners and redistributed to the peasants had taken place shortly after the communists had come to power.
Collectivisation, where peasants lost their own pieces of land and instead worked for wages on land owned by the state had also begun to take place.

Mao believed this was not enough to expand both agricultural and industrial production and instead introduced the second five-year plan in 1958.
This would become known as the ‘Great Leap Forward’.

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Credit:
Created by Daniel Turner

Narrator:

Chris Kane
https://vocalforge.com/

Music Credit:
Decline by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/r....oyalty-free/index.ht
Artist: http://incompetech.com/



Sources:
Tombstone. The Untold story of Mao’s Great Famine.
By Yang Jisheng.

Red Inc.: Dictatorship and the Development of Capitalism in China, 1949-2009
By Robert K. Schaeffer

Socialism in China (1919-1965)
By Yu Youjun

Mao's Great Famine: The History of China's Most Devastating Catastrophe, 1958-62
By Frank Dikötter

The Great Famine in China, 1958-1962: A Documentary History

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Thanks to the technological advances of the modern age, in 2023 life is pretty safe. In the past however, many of the things we take for granted now were likely a death sentence for our ancestors.


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Credit:
Show Created by Daniel Turner (B.A. (Hons) in History, University College London)
Script: Jake Leigh-Howarth

Narrator:

Chris Kane
https://vocalforge.com/

Backe, Caleb. "Deadly Beauty Practices In History." 6 March, 2022. Maple Holistics.

BAUS. "Virtual Museum Time Corridor 17th Century". Accessed 27 February, 2023.

CDC. "Syphilis: The Facts." Accessed 27 February, 2023.

CTPA. "Cosmetic Safety." Accessed 27 February, 2023.

De Abreu, Kristine. "Apocalypse Then: The Volcanic Winter of 536AD." July 18, 2022. ExplorersWeb.

Degroot, Dagomar. "Small climate changes can have devastating local consequences – it happened in the Little Ice Age." July 27, 2021. The Conversation.

Eschner, Kat. "Fearing a Smallpox Epidemic, Civil War Troops Tried to Self-Vaccinate." May 1, 2017. Smithsonian.

Finance. "Scotland to Panama Flight Duration." Accessed 27 February, 2023.

Greschko, Michael. "Colossal volcano behind 'mystery' global cooling finally found." August 23, 2019. NationalGeographic.

Grist, Kerry. "Dangerous Beauty: Hazardous Chemicals and Poisons in Historic Cosmetics." 29 July 2022. ScienceMuseumGroup.

Johnson, Ben. "The Darien Scheme." Accessed 27 February, 2023.

Kelly, DB. "The Deadly Great Frost of 1709 Is Still a Mystery." Last modified 13 January, 2022. Grunge.

Lanchester, John. "How the Little Ice Age Changed History." March 25, 2019. The New Yorker.

Laumonier, Lucie. "A Medieval Peasants’ Winter." rused 27 February, 2023.

Maley, Sonny. "The Darien Scheme." May 2005. GLA.

Maloney, T.R., Dilkes-Hall, I.E., Vlok, M. et al. "Surgical amputation of a limb 31,000 years ago in Borneo." Nature 609 (September 2022): 547–551.

Oosthoek, K. Jan. "Little Ice Age." June 5, 2015. EH Resources.

Pattenden, Miles. "Volcanoes, plague, famine and endless winter: Welcome to 536, what historians and scientists believe was the ‘worst year to be alive'." February 1, 2022. The Conversation.

Seladi-Schulman, Jill. "What Is the Periosteum?" Last modified September 26, 2018. Healthline.

Shuster, Sam. "Painless amputation: history of a discovery
that wasn’t made." BMJ (19-26 December 2009).

Smith College. "The Effects of the Little Ice Age (c. 1300-1850)." Accessed 27 February, 2023.

Wischhover, Cheryl. "The Most Dangerous Beauty Through the Ages." December 17, 2013. TheCut.

Zapata, Mariana. "How Civil War Soldiers Gave Themselves Syphilis While Trying to Avoid Smallpox." November 30, 2016. Atlas Obscura.

A rise of protests by students and workers waving Hungarian flags with the communist emblem in the centre cut out arose in Budapest, erupting into active fighting in October 1956.

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Credit:

Narrator:

Chris Kane

http://ckvox.com/

Animation:
Daniel Turner

Artwork:
Daniel turner

Logo of the Warsaw Treaty Organization of Friendship, Cooperation, and Mutual Assistance

CC BY-SA 3.0

Fenn-O-maniC - Own work

https://creativecommons.org/licenses/by-sa/3.0/

Music Credit

The Descent Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/by/3.0/

#shorts

This statistics video tutorial explains how to make a histogram using a frequency distribution table.

Introduction to Statistics: https://www.youtube.com/watch?v=XZo4xyJXCak

Arithmetic, Geometric, & Harmonic Mean:
https://www.youtube.com/watch?v=6G6i8vSa8Zs

Simple Frequency Tables:
https://www.youtube.com/watch?v=lyRbCwDDnJo

Relative Frequency Distribution Table:
https://www.youtube.com/watch?v=gq3FPpm2yvA

Cumulative Relative Frequency Table:
https://www.youtube.com/watch?v=6hJGa4Zp62M

_________________________________
Dot Plots and Frequency Tables:
https://www.youtube.com/watch?v=Iu17mY1VfZU

Stem and Leaf Plots:
https://www.youtube.com/watch?v=MUCvUgGfzdo

Side By Side Stem and Leaf Plots:
https://www.youtube.com/watch?v=wkAjnGmRPVo

Histograms:
https://www.youtube.com/watch?v=AndS0RLdxtk

How To Make a Frequency Polygon:
https://www.youtube.com/watch?v=y7Wb9AjbRjo

__________________________________
Quartiles, Deciles, & Percentiles:
https://www.youtube.com/watch?v=40o82o3uNfk

Interquartile Range & Outliers:
https://www.youtube.com/watch?v=STSP8gTSdT8

Skewness & Symmetric Distribution:
https://www.youtube.com/watch?v=U0NZu6f5TMI

Sample Mean and Population Mean:
https://www.youtube.com/watch?v=cmtBUWCC-6A

Mean, Median, & Mode - Grouped Data:
https://www.youtube.com/watch?v=zjHfAhcU6kE

____________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/

This Statistics video tutorial explains how to find the probability of a binomial distribution as well as calculating the mean and standard deviation. You need to know how to use the combination formula in order to solve the example problems presented in this video.

Introduction to Probability:
https://www.youtube.com/watch?v=SkidyDQuupA

Probability Formulas:
https://www.youtube.com/watch?v=bddckR734aM

Probability Explained:
https://www.youtube.com/watch?v=UORztmWGY6Q

Probability With Geometry:
https://www.youtube.com/watch?v=DeH5aHWxEaI

Probability of Complementary Events:
https://www.youtube.com/watch?v=0T-CaQCiSf4

Conditional Probability:
https://www.youtube.com/watch?v=sqDVrXq_eh0

__________________________________
Independent and Dependent Events:
https://www.youtube.com/watch?v=lWAdPyvm400

Probability of Mutual Exclusive Events:
https://www.youtube.com/watch?v=X6usGgwXFyU

Multiplication and Addition Rule:
https://www.youtube.com/watch?v=94AmzeR9n2w

Compound Probability:
https://www.youtube.com/watch?v=EHU6pVSczb4

Expected Value:
https://www.youtube.com/watch?v=b6VK2VPMXNI

Probability Tree Diagrams:
https://www.youtube.com/watch?v=w4wKXVwtGac

___________________________________
Bayes Theorem:
https://www.youtube.com/watch?v=OByl4RJxnKA

Probability - Binomial Distribution:
https://www.youtube.com/watch?v=3PWKQiLK41M

Probability - Geometric Distribution:
https://www.youtube.com/watch?v=d5iAWPnrH6w

Probability - Poisson Distribution:
https://www.youtube.com/watch?v=m0o-585xwW0

Continuous Probability Distributions:
https://www.youtube.com/watch?v=QxqxdQ_g2uw

Probability Density Functions:
https://www.youtube.com/watch?v=3xAIWiTJCvE

__________________________________
Probability - Uniform Distributions:
https://www.youtube.com/watch?v=KfunVw-0AH0

Probability - Exponential Distributions:
https://www.youtube.com/watch?v=J3KSjZFVbis

Probability - Normal Distributions (Calculus):
https://www.youtube.com/watch?v=gHBL5Zau3NE

Probability - Standard Normal Distributions:
https://www.youtube.com/watch?v=CjF_yQ2N638

Probability - The Law of Large Numbers:
https://www.youtube.com/watch?v=ihTpK6dXSas

___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

This math video tutorial provides a basic introduction into ratio and proportion word problems. Here is a list of examples and practice problems:

Percentage Word Problems: https://www.youtube.com/watch?v=kjpwBu6DmkM

Unit Rates, Ratios, & Proportions:
https://www.youtube.com/watch?v=s0RBRkehzwo

Ratios and Proportions - Word Problems:
https://www.youtube.com/watch?v=JOZSFwuyqok

Ratios and Proportions - SAT Math:
https://www.youtube.com/watch?v=Y4fgwWEGQlg

Ratios and Proportions - Mean & Geometry:
https://www.youtube.com/watch?v=tFCrFa0mDi4

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Acid Mixture Word Problems:
https://www.youtube.com/watch?v=e2FAAMlAJ3c

Translating Words to Algebraic Expressions:
https://www.youtube.com/watch?v=QEnFIgN8UBw

Words to Equations - More Problems:
https://www.youtube.com/watch?v=VjPX-XlN7Ok

Consecutive Integers Word Problems:
https://www.youtube.com/watch?v=hPnoxAf60c0

Age Word Problems - Past, Present, Future:
https://www.youtube.com/watch?v=7x7Hl9ztYbk

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Final Exams and Video Playlists:
https://www.video-tutor.net/