The Formula for Taylor Series

Note: Taylor Series when a=0 is called Maclaurin Series, but they are all power series anyway. This video shows how to compute the taylor coefficients.
Taylor Series for e^x: • 11.10 (Part 2) Power S...
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Geometric Series: • Geometry Series
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blackpenredpen | 曹老師

[@ArtStyleEdge]

Man i was about to sleep..Nevermind i will watch this first!

[@alexandrebriard9175]

When you watch this video after 3B1B : *you know i'm kind of a mathematician myself*

[@aaronaugust7904]

I know it is pretty randomly asking but does anybody know a good site to stream newly released series online?

[@franklindrake3225]

@Aaron August I dunno atm I've been using Flixportal. Just google for it =) -franklin

[@aaronaugust7904]

@Franklin Drake thanks, I went there and it seems like they got a lot of movies there :D I appreciate it !!

[@franklindrake3225]

@Aaron August no problem xD

[@Draginx]

This guy is awesome, I love maths, physics, and engineering, and this guy explains everything so great!

[@benjamingiribonimonteiro9393]

Thanks for featuring me at the beggining! Love your channel

[@blackpenredpen]

Benjamin Giriboni Monteiro : )))

[@benjamingiribonimonteiro9393]

@@blackpenredpen :)

[@CalculusPhysics]

i think the thumbnail has a slight typo, shouldn’t it be n! in the denominator, not simply n?

[@diabolicallink]

Chloe I thought so too

[@baoradeon878]

Love the way he explained how does the Taylor series work. THANK YOU

[@suellenalmeida3040]

I have been loving your videos! Thank you so much :D

[@kendalwilliams5128]

I loved how you explained it. Thanks!

[@ski34able]

I am soooo glad I clicked no this video! Best explanation on youtube so far

[@OLApplin]

:O ! FOURIER SERIES ! I just can't wait (my favorite math subject ever)

[@sayhan3631]

Amazing video ! I enjoyed watching it

[@____Paul____]

I appreciate that you started with showing the usefulness of Taylor Series before diving into the details of how to use it! Edit: This video is only showing the formula, not how to work with Taylor series.

[@ArhamKhan05]

thats amazing sir great explanation thanks ❤

[@math4math608]

Hopefully, Fourier Series will be AS GOOD AS THIS VIDEO! Thanks, Very Detailed Explanation!

[@ragnarlothbrok4090]

Thanks! You got me through High School!!!!

[@quantumcity6679]

Awesome job... I'm curious about next video 😘

[@angelmendez-rivera351]

Papa Taylor has blessed us.

[@benjaminbrady2385]

Can't wait for that Fourier series video!

[@KotaCraig]

I hope you know how many people you've helped! Thank you!

[@PrynPucksomporn]

Finally, this vid is 10x understandable than my lecture

[@AlessandroZir]

good! the comparison with decimals was very useful;

[@emrealpozavc783]

Thank you, can you make a video about lagrange error bound ?

[@moaydsparklug8311]

Hi I'm physicist , fall in love with taylor series helped me alot of times ,anyway I like your videos 😁

[@djchavaz]

For 1/(1-x) expansion using infinite geometry series is true when -1

[@BenjaminKeilty]

For anyone curious about the "unless you add a circle" comment at 0:40: The mediant en.m.wikipedia.org/wiki/Mediant_(mathematics) is pretty cool and useful in math competitions if you know how to use it

[@abhilashsaha9931]

You are God.

[@eustacenjeru7225]

good explanation

[@slayervii2280]

First I was like why is the first term of the series in the thumbnail equal to infinity then I realised there was no factorial sign on the "n"

[@aphelmusonda5253]

youre a hero sir, thank you

[@khalilmohammed2297]

Thank you so much

[@guliyevshahriyar]

thanks a lot

[@rob876]

1/2 an hour plus a 1/3 of an hour = 30 mins plus 20 mins = 50 mins = five sixths of an hour. 0.83333... = 8/10 + 1/30 = 48 mins + 2 mins = 50 mins.

[@iremkarakas6770]

this man i really love you .

[@jamesoneill5070]

This formula was developed by Brook Taylor, an English mathematician (1685-1731) so it's over 300 years old.

[@nafissaatlagh206]

Hell we need a love reaction in youtube 😐❤

[@roshannanayakkara5865]

Excellent

[@ggssjoker4931]

TQVM

[@manuelodabashian]

Thanks!

[@alejrandom6592]

3:04 e^x + sinx "can't even do the common denominator" *laughs in complex definition*

[@ado22222]

but where did he get the sinx from?

[@alejrandom6592]

@@ado22222 from his imagination

[@ado22222]

@@alejrandom6592 oh ok so its not like he is saying 1/1-x somehow equals to sinx right? Cool Because i though he meant that and it was really driving me nuts

[@alejrandom6592]

@@ado22222 yeah don't worry it was just an example ;)

[@dr.rahulgupta7573]

Excellent presentation Sir.Thanks with sincere regards. DrRahul Rohtak India

[@phorusrhacidaeaves811]

can anyone help to explain what he said 'best friend' on 4:57 to be?😅😅😅

[@gediman0512]

you are a great man..keep it up...in addition to this I would asked you one thing.I would like to physics could you announced the best lecturer for physics like you..

[@albatrosslove8654]

there is summation (n=o to inf ) but you are diff n -times means this is finite then how can we take the limits upto inf

[@abtahi._]

beautiful

[@XESolar]

So good!

[@Patapom3]

Amazing!

[@poornimabalachandran1004]

Good job👍👏👏

[@louisecaustur7996]

that was beautiful :o

[@pratikmanurkar9421]

Nice

[@torung9606]

omggg i love youuuu

[@jibran8410]

so using that f^0 (a) = 0! x Cn can you say that Cn = f(a) ? where n is 0

[@principiamathematica5414]

When the note becomes notice!

[@iamimran5880]

Very nice sir live from India

[@loukafortin6225]

Nice video there! I'm one year ahead of my first classes of calculus, so I'm having a hard time to find a way to calculate the arc length of the function f(x)=x^3. I can't get pass the step : int of sqrt(x^4+1/9)dx. Please help xO. I definitely KNOW there's a way arghhh and it's haunting me lol

[@angelmendez-rivera351]

Unfortunately, you cannot find the antiderivative of this function in terms of single-variable elementary functions. There is just no answer you can give using arithmetic operations, exponents or powers, trigonometric functions, hyperbolic functions, or the inverses or compositions of any of the above. Wolfram Alpha gives an answer that requires imaginary numbers and uses special elliptical integrals.

[@loukafortin6225]

@@angelmendez-rivera351 oh okay! I needed this to stop getting upset of not finding anything. 'guess I shouldn't mess with those things too much. Anyways, thanks!

[@sebastianmeier5002]

🔥🔥🔥

[@bogdancorobean9270]

One thing I don't quite get is how do we know we can represent functions as power series. I mean, why would someone 200 years ago or whenever would have thought of trying something like this? I know it works out, but it seems so unintuitive. Same for power series solutions to differential equations.

[@zahraa-dm5cy]

0:09 my goal for this year .......

[@bigalturn1]

can you derive the Lagrange Error Bound formula please

[@armandoski-g]

7:45 you're an all star

[@gourabghosh5574]

A circle of radius 1 cm rotates and move like a wheel around another circle of 3 cm radius and returns to its initial position. How many times does the citcle of radius 1 cm rotate? The answer is 4. Explain why it is not 3 ie Problem with the solution (circumference of the bigger circle/circumference of the smaller circle)

[@Wecoc1]

You want us to make your homework, pal?

[@MrHK1636]

Hello, I need help in this problem: If there is a polynomial such that f(x+5)=f(5-x) with 4 real roots. How should you calculate sum of all roots. Don't tell me what answer is. I want a little hint 😅

[@MrHK1636]

And that condition is true for all real values of x

[@snillie]

Since f(x+5)=f(5-x), that means if r_1 and r_2 are roots, you can immediately know what the other two roots are (assuming that knowing r_1 doesn't lead you to r_2 and vice versa). If you can find the other two roots, you should be able to solve the problem c:

[@MrHK1636]

Thank you, right answer is 20, isn't it?

[@omkarsinghchauhan3053]

i love that thing he holds in his hand btw it is mike or anything else

[@angelmendez-rivera351]

Omkar Singh Chauhan it is a Mike

[@ado22222]

sorry dumb question. why would 1/(1-x) become sinx at 3:03

[@cleahey6350]

love you x

[@user-ki4hu8fq9g]

U the GOAT Saludos a toda la raza de la FESC

[@alejandroiglesiasllobet3133]

0:40 “unless you have a circle right here” ??? I’m so confused

[@tpstrat14]

the main problem you had in that moment is that you didn't hear him say "let's not talk about that". He shouldn't have even mentioned it LOL. Because of course anything in math can be expanded on. ANYTHING. In other words, you can always get confused at any point if the teacher tries to expand the idea beyond what you're ready for.

[@abhilashsaha9931]

Look up the word "mediant"

[@AlbinoJedi]

Can you explain setting a=0 or any other number and why? I don't get the "centering".

[@dawsonbowhay6796]

A Taylor series is infinite, but in practice we may only use the first few terms of the Taylor series as a close approximation to the true function. Therefore, all the [infinite] remaining terms that aren't used are equal to the error between the approximation and the true function. If you graph the true function and the approximation, you will see that there will be zero error at x=a, but as x gets further away from the value a, the error increases. You might choose a certain value of a based on which values of x you want your approximation to be accurate for. Or, you might have to use a non-zero value of a if the function is undefined at x=0 (take for example y = 1/x, where you can't divide by zero so a=1 would probably be used).

[@wuwu1598]

Thank you, father

[@JureRatkovic]

"Let's look at the jerk of that... no just kidding"

[@oil1263]

this guy is fking underrated,

[@sajankumarkar8237]

Shouldn't 1/2 + 1/3 be 5/6?

[@ayoubsbai6339]

i love you :)

[@Kumar-oe9jm]

How to kill a constant? bprp 2019: by integration

[@y.z.6517]

How to kill a positive number? By differentiation.

[@opufy]

5:15 Taylor (the dad) series haha

[@alejandroiglesiasllobet3133]

"My biggest goal to 2020 is to get selected to the Brazilian team in IPhO 2021"

[@akyberdiew8797]

👏

[@charleswoodard8478]

Astounding how little attention this material attracts as opposed to more high concept rigamarole and dramatized frivolities done in the name of fame. This should depose the current mainstream passtimes, we’d be far better off…

[@ssdd9911]

4ier series next?

[@blackpenredpen]

s sdd Yup, I call it fouryay

[@gregoriousmaths266]

Lol fouryay

[@cptn_n3m012]

Can you integrate the gamma function ?

[@angelmendez-rivera351]

leo bonneville You can, you simply cannot express it in terms of any other well-studied functions, as far as I understand. At best, you can numerical approximations for the definite integral, and the indefinite integral can only be expressed as the definite integral of another function, which is itself not solvable in terms of elementary functions.

[@SoyFerchow]

I love you.

[@douro20]

Is it the same Taylor for whom the Taylor Manual is named?

[@carultch]

It's named for Brook Taylor

[@maginobionrequiem9167]

COMEDY KING XD

[@xylellaa]

I love you

[@clubstepdj]

you call it "the dad", papa flammy call it "papa taylor"

[@MozwGamer]

If I fail Calculus 3, I'll a top subscriber by next year

[@user-or9fo5ym6h]

1

[@angelmendez-rivera351]

Mr. Cao, I have a number theory challenge for you. Consider the pair of numbers n - k and k + 1, where n is a natural number and k = 0, 1, ..., n - 1. For what values of n are n - k and k + 1 co-prime (relatively prime, they share no common factors) for all k? In other words, for what values of n is gcd(n - k, k + 1) = 1 for all k satisfying the conditions I established?

[@TIENTI0000]

Гениально

[@user-wu8yq1rb9t]

You can find any relation between Taylor (the mathematician) and Taylor (the singer; Taylor Swift) ?!! *Taylor Series* and *Taylor Swift* !!?

[@carultch]

That's most likely just a coincidence. The Taylor series is named after Brook Taylor.

[@jurihorstmann645]

To sad that she stopped making proofs to start a music career. Taylor Swift is a math genius!

[@carultch]

This is named after Brook Taylor. A completely different person.

[@giuseppeagresta1425]

​@@carultchit's a joooooke

[@epicsushi5817]

@@carultchr/woosh

[@macglone]

That was physically painful. Well done!

[@yaxeenrahman]

2^X + 3X=7 Solve this one algebraically without Graph.

[@angelmendez-rivera351]

Yaseen Rahman 2^X = e^(X Ln 2). Then e^(X Ln 2) + 3X = 7 => e^(X Ln 2) = (7 - 3X) => 1 = (7 - 3X)e^(- X Ln 2). Now multiply the equation by Ln(2)/3 to get Ln(2)/3 = [7Ln(2)/3 - Ln(2)X]e^[-Ln(2)X]. Multiply the equation by e^[7Ln(2)/3] to get 2^(7/3)•Ln(2)/3 = [7Ln(2)/3 - Ln(2)X]e^[7Ln(2)/3 - Ln(2)X]. Now apply the Lambert W function to the equation to get W[2^(7/3)•Ln(2)/3] = 7Ln(2)/3 - Ln(2)X => Ln(2)X = 7Ln(2)/3 - W[2^(7/3)•Ln(2)/3] => X = 7/3 - W[2^(7/3)•Ln(2)/3]/Ln(2), and this is the exact form of the answer you wanted, solved using nothing but algebraic, exponential, and the Lambert W functions.

[@yaxeenrahman]

@@angelmendez-rivera351 thank you so much ❤

[@oscartroncoso2585]

First!

[@blackpenredpen]

Yup, you got it again!

[@subhopal]

FIND OUT THE DERIVATIVE OF x! WRT x

[@subhopal]

If f(x)=x! then, f'(x)=?

[@subhopal]

Find the derivative of factorial x wrt x

[@yoavcarmel1245]

it is something with the gamma function, you cannot get a nice solution for that :(

[@srpenguinbr]

x! is a discrete function Unless you consider the Pi function, which does give an answer, but in terms of improper integrals or other special functions

[@srpenguinbr]

If you don't consider the pi function, then x! is not differentiable.

[@BlokenArrow]

1/2 plus 1/3 does equal 2/5 in statistics.

[@angelmendez-rivera351]

BlokenArrow How?

[@bullinmd]

Cantor proved it is impossible to "count" real numbers.

[@matj12]

A note for 1:13: If you find it hard to remember the digits of 1/3, there is a mnemonic for the first 25 digits: kzbin.info/www/bejne/hJrRo4eNZqeraLs

[@blackpenredpen]

Hahaha, nice!!!!

[@user-or9fo5ym6h]

Hi, go int 1/(x^n+a^n)dx, n=2k, n=2k+1

[@angelmendez-rivera351]

Алексей Шубин Not a particularly special exercise or problem. Since a is an arbitrary real number, we know there exists some b such that b^(2k) = a^(2k + 1). This simplifies the problem to anti-differentiating 1/(x^(2k) + b^(2k)).

[@user-ps1dm4fc4l]

1/2+1/3=5/6 no 2/5 :) 0:32

[@mainaak3794]

First comment!

[@tarekhajjshehadi4670]

Do you know what's so special about the number 1729?

[@blackpenredpen]

Tarek Hajjshehadi yes

[@AndDiracisHisProphet]

yes

[@marcellomarianetti1770]

Yes, we all know

[@ironmc7972]

1729 can be written in sum of 2 cube numbers in 2 ways. 1729=12^3+1^3 and 1729=10^3+9^3

[@user-dz1px2mc7o]

@@ironmc7972 That's right, but what makes 1729 so special is that it's the smallest number that can be written as a sum of two cubes in two different ways

[@OonHan]

1/2 + 1/3 is not 2/5 :(((

[@PhilBoswell]

There is a specific operation which does in fact work this way, but the name escapes me right now. The operation which combines a/b and c/d to give (a+c)/(b+d) has the interesting property that it guarantees a new fraction which lies between the two source fractions and is very helpful in various proofs, the nature of which also escapes my memory right now. Look, it's Friday and it's been a tiring week, OK? Somebody else pick up the thread? ;-)