Taylor Series and Maclaurin Series - Calculus 2

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  • Опубліковано 21 січ 2025

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  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +34

    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
    Next Video: ua-cam.com/video/V1AKAkGJlN8/v-deo.html

  • @ericplz7420
    @ericplz7420 6 років тому +2026

    Sir, you deserve my college tuition, my college doesn't deserve a single penny when all they do is write a fricking textbook on the chalkboard and expect to know everything. Thank you for every single thorough explanation and giving many examples so that I can understand.

    • @monicagarza1761
      @monicagarza1761 6 років тому +9

      rt

    • @Sneaky1ne
      @Sneaky1ne 6 років тому +90

      part of being a good student is also learning for yourself by looking for proper sources, such as this one, but be certain that a true understanding of the matter is not achieved by watching this video alone, although it does bring us a long long way ahead of just the school lectures. Also, exposure in class combined with these videos is much more effective than just the videos. Make no mistake this guy also maybe saved my finals

    • @tacosamuel
      @tacosamuel 6 років тому +4

      3 months ago, hmmm. I'm in the same situation as you. What college do you attend?

    • @isaacdamon26
      @isaacdamon26 4 роки тому +1

      facts

    • @f4ux578
      @f4ux578 4 роки тому +1

      why yall learning this in college im in highschool and we have to learn this b u l l s h i t

  • @coenvanbeelen3746
    @coenvanbeelen3746 6 років тому +901

    So i have a calculus test tomorrow and no professor has ever made me undestand this.
    I watched this video and it's completely clear.
    You're worth you weight in gold man

    • @tacosamuel
      @tacosamuel 6 років тому +5

      Oh yeah yeah, understanding math is great.

    • @HypCarlos
      @HypCarlos 5 років тому +5

      @@tacosamuel Why does everyone have the Arnold pic? I am confused

    • @tacosamuel
      @tacosamuel 5 років тому +13

      @@HypCarlos a youtuber named Maximilianmus told his subscribers to switch their profile pictures and spam comment sections. It has since ended, but some people still have them on.

    • @brandondunn6838
      @brandondunn6838 5 років тому +1

      Oh yeah yeah

    • @garyzhuang5894
      @garyzhuang5894 5 років тому

      @@tacosamuel I always thought thats a picture of Postal's Dude

  • @averyrobinson4666
    @averyrobinson4666 3 роки тому +247

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  • @sarahvincent6144
    @sarahvincent6144 6 років тому +520

    Thank you for explaining a week of my calc class in 30 mins and helping me pass my finals. You are a true hero.

  • @dysmaruuramsyd3233
    @dysmaruuramsyd3233 4 роки тому +148

    I didn't have even the slightest bit of intuitive understanding of Taylor Series expansion from 3 hours of reading my textbook. This one single video explained the entire concept perfectly. You're an absolute lifesaver man.

    • @lucaskincanyon7393
      @lucaskincanyon7393 2 роки тому +6

      Same. That's why I'm here at 2AM prepping for my calc quiz tomorrow at 6:30 PM. :,,,)

    • @issajoke220
      @issajoke220 2 роки тому

      @@lucaskincanyon7393 so did u pass?

    • @lucaskincanyon7393
      @lucaskincanyon7393 2 роки тому +3

      @@issajoke220 no I go a 52% Lmaooo

    • @EliteCubingAlliance
      @EliteCubingAlliance Рік тому +5

      ​@Lucas Kincanyon Yeah, if you are watching at 2AM You're basically screwed

  • @kxngmar2748
    @kxngmar2748 4 роки тому +1196

    0:00 Taylor series for function f(x)=ln(x) centered at a=1
    7:14 Taylor series for function f(x)=e^x centered at a=3
    10:49 Maclaurin series for function f(x)=sin(x)
    17:05 Maclaurin series for cos(x) using Maclaurin series for sin(x)
    23:02 Maclaurin series for cos(x^2)
    24:28 Maclaurin series for xcos(x)
    25:30 Maclaurin series for function f(x)=x^2 e^(-x)
    27:31 Maclaurin series for function f(x)=cos^2x

  • @khalidjamal3848
    @khalidjamal3848 4 роки тому +178

    19:12 The Organic Chemistry Tutor breaks character !!!!

    • @DaniyalX
      @DaniyalX 3 роки тому +53

      lmaoo he sounded so pissed off

  • @akueijohnsonateny
    @akueijohnsonateny 2 роки тому +58

    I just took 15 minutes of my life just to understand what really makes you the best tutor of all time, and one thing I discovered is that you assume the learners know absolutely nothing. This is what it means to be a perfect teacher; to know that people might not know what you know. You explain every piece of your work, including what makes the difference between 2 and 1 equals 1. Because of you, I don't go to Math class frequently because I know there's a better class on UA-cam. God Bless You, Sir!!!!

  • @smorris5296
    @smorris5296 6 років тому +3056

    I owe all of my final grades to this man and adderall

  • @colleenbungard9476
    @colleenbungard9476 Рік тому +7

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  • @nolapickering1917
    @nolapickering1917 3 роки тому +14

    My AP calc test is in 3 days. This is the first time I've thoroughly understood this topic. You, sir, are a god next to the American education system

  • @tyscott4949
    @tyscott4949 3 роки тому +4

    I find it funny that I come across " The Organic Chemistry Tutor" -- and listen to a "tutor" run circles around calculus instructors on UA-cam and in the classroom teaching calculus II.
    I have spent about an two hours or so taking notes reading reference calculus books and digesting the Taylor Series and at the same time find it soothing that things are becoming clear, what once was amiss, in the midst of the fog.
    Thank you, I will join the page when I start my calculus class this summer of 2022.

  • @vardhanadhikari5510
    @vardhanadhikari5510 5 років тому +12

    Dude, you're not only AP tutor but an IB tutor as well. God bless this man.

  • @phantom4902
    @phantom4902 3 роки тому +43

    Sir, you're a gem, this was the topic I was facing the most difficulty with and you made it look so simple. Thank you for existing

  • @GamingWithMicc
    @GamingWithMicc 5 років тому +27

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    • @aurumstinger4479
      @aurumstinger4479 3 роки тому

      How is it so far?? I am also doing first year in CompSci

    • @GamingWithMicc
      @GamingWithMicc 3 роки тому

      @@aurumstinger4479 Hectic bro

    • @zadsand
      @zadsand Рік тому

      How is it now bro? now I'm doing the first year in Computer Science

    • @GamingWithMicc
      @GamingWithMicc Рік тому +6

      @@zadsand I’m a software engineer at Amazon now. Thanks for bringing me back here

    • @chinyeamprecious
      @chinyeamprecious 10 місяців тому

      Hello
      I'm also a computer science student

  • @abigailreimer-golden8856
    @abigailreimer-golden8856 Місяць тому +2

    Dude you are the only reason I passed calc II I swear. I love you so much

  • @lesegomokgabudi5798
    @lesegomokgabudi5798 5 років тому +43

    i had no idea on how to solve Taylor series and its younger brother Maclaurin series....but now i have an idea. Thanks a lot my brother

  • @vhiedkc859
    @vhiedkc859 5 років тому +21

    My A’s in maths n physics are from you sir not our boring unclear professors.
    Much love you really deserve my tuition fee & extra pay.
    Asante sana. 🙏🏽

  • @Justreemm
    @Justreemm 2 роки тому +26

    Sir I love you with literally every fiber of my being

  • @xb5959
    @xb5959 3 роки тому +20

    I've been watching your videos since high school, and now I'm in college taking up Biochemistry and I'm still watching your vids for most of my subjects and it has helped me a lot in ways my professors could not. It's been difficult to learn in classrooms and online classes bc I have inattentive type ADHD but these lecture videos keep me going. Thank you very much for this. I will repay when I finish my degree and land a decent job. I have one suggestion though, which is to have lecture notes from the examples to be available online because it's difficult to take notes from the video, but this is mostly because I'm cramming and I do not have much time to take notes but I need to. Thank you and please continue to do this.

  • @42laar
    @42laar 2 роки тому +3

    wow, i've been taught taylor's series in class, review sessions, recitations, and youtube videos. this explanation is by far the best one at helping me understand it. i feel much more confident about taylor's series now. thanks a lot!

  • @watertantrums2000
    @watertantrums2000 4 роки тому +51

    I lost it @ 19:13. Him expressing his frustrations other than math and science equations is >>>. Dead XD

  • @HK-ez8vm
    @HK-ez8vm 3 роки тому +10

    can't be skipping ads cuz this man has been carrying my carrier.

    • @iqrakhanamansari8670
      @iqrakhanamansari8670 3 роки тому

      Hey is this 'TAYLOR SERIES' taught in high schl or clge in the US??

    • @Arnie3
      @Arnie3 9 місяців тому

      @@iqrakhanamansari8670both depending on your level of math

  • @connectingspyyo8159
    @connectingspyyo8159 3 роки тому +14

    i took calc 2 almost 2 years ago and I am super worried about calc 3! Thank you so much for this, as it is a great refresher. I feel like you taught this better than my professor did at the time

    • @HanOnkel
      @HanOnkel 2 роки тому +13

      Gee, calc 3 factorial? What is that even about?

    • @default3623
      @default3623 2 роки тому +4

      @@HanOnkel Lmao😐

    • @ulasdevrim7492
      @ulasdevrim7492 2 роки тому +5

      @@HanOnkel calc6, the ultimate calc

  • @danielcash1037
    @danielcash1037 9 місяців тому

    Words don't describe. Thank you very much. In your explanations, you don't do large algebraic simplifications which make it difficult to understand the logical process on the fly and I appreciate that. I'm not sure why every other teacher I've had does it because it is not helpful when learning a new topic. You consistently teach and ensure you go through each explanation thoroughly. You make a good assumption of prior knowledge in your videos and give lots of examples to solidify the learning. I think you're videos are perfect, the best I've seen. Thank you very much.

  • @xoxo__diana
    @xoxo__diana 6 років тому +17

    I want to thank you so so much! my professor and IA made this series so hard to understand during lecture/discussion, but you made it so easy to understand!

  • @shubox
    @shubox 6 років тому +2

    you are the best. 30 minutes of this is better than 2 hours of my actual class

  • @chukwumandive9597
    @chukwumandive9597 Рік тому

    All I can say is WOW!! Thank you so much. You have no idea the amount of knowledge you're dishing out there. I can now boldly flex my new found powers in solving Taylor and Maclaurin series. You are a life saver.

  • @ronak859
    @ronak859 3 роки тому

    whoever is making these videos, bless you man

  • @jacquelinet9109
    @jacquelinet9109 5 років тому +269

    i’m watching this video to put myself to sleep and i have accidentally learned things

  • @jelome_x
    @jelome_x 3 роки тому +2

    You just removed the frustration I had with this topic. Now I can smile. Thank you.

  • @thomasblackwell9507
    @thomasblackwell9507 Рік тому +1

    It has been close to 40 years since I first started using this stuff but it still is amazing to see how much it is worth knowing!

  • @Alejandro-mo4pt
    @Alejandro-mo4pt 24 дні тому

    This guy is a genius!!! This might be basic calculus , but the way he explain it, is just perfect. He makes it easy

  • @incredibleplanet
    @incredibleplanet 5 років тому +2

    my First comment just for this guy to know he is saving lives! READ IF YOU WANNA PASS CALC 2 .........at my college half of the people fail this class and i was sure that i was gonna fail this class taking it over the summer with other class( chem 2) but with you and God i passed it with a B woohoo! with you and God I passed chem 1,2 , Physics, calc 1,2. and taking organic next semister! for people who are strugling, i am truly duuuumb at math and i took it over the summer because i know he has videos. so what i did was study 7 hours a just for calculus 2! and before the exam i study/revewed 25-30 hours so for this class 49 hours a week + 30 hours of review before the exam lol. do what i did and you will pass, i did not care about life until i passed calc 2! i did not wanna take it twice so i worked harrd! THANK YOU my tutor!

  • @mahyarkharazi1360
    @mahyarkharazi1360 10 місяців тому

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  • @EnjoimentProductions
    @EnjoimentProductions 9 місяців тому

    Thank you! The part that helped me most is when you are making the summation notation of the function. Your red notes show what part of the expression is n = 0, n = 1, n = 2, n = 3, n = 4 @ 10:04 . This was so helpful. I could not find any visual in my textbook that showed what part of the expression relates to which n. But you laid it out in red and that helped me make sense of it all. Thank you again!

  • @Mai-ml7lb
    @Mai-ml7lb 7 місяців тому +380

    ngl, i might be cooked.

  • @elaine6060
    @elaine6060 4 роки тому +6

    this covers everything about the calculation of Tylor series! Amazing!

  • @sethkirotichdauphin1784
    @sethkirotichdauphin1784 5 років тому +7

    you know what................ you are the best thank you so much i now get the simplicity of this unit!!!!!!!!!!!!!!!!!!!!

  • @willpizzo3629
    @willpizzo3629 5 років тому +1

    holy cow dude i have a calc test tomorrow and you just saved my life. you are a true genius thank you so much

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    @gboyawesome1159 3 роки тому

    This guy is the GOAT! He deserves way more subscribers !

  • @kristineopenshaw6415
    @kristineopenshaw6415 4 роки тому +2

    I'm able to work on my homework not by reading the prescribed textbook but by watching these videos. Thank you so much!

  • @constance5004
    @constance5004 3 роки тому +4

    online school has been so tough for me you're literally the reason i'm passing calc rn ily

  • @alisonalexander9057
    @alisonalexander9057 5 років тому +5

    Once again the Organic Chemistry Tutor has come through!

  • @karolinshikam7919
    @karolinshikam7919 5 років тому +2

    man you deserve Heaven because you're serving AND saving the universe.

  • @oswilmathematics
    @oswilmathematics 4 роки тому +4

    Thanks for taking into consideration every little details. You made me understand Taylor and Maclaurin Series very well.

  • @crustyflamingo1023
    @crustyflamingo1023 9 місяців тому

    Just hearing this man's voice assures me that I will be ok for my class, thank you so much!

  • @alpharibo
    @alpharibo 2 роки тому +1

    Watching this on my train ride to school before a quiz, thank you thank you thank you

  • @zettabyte212
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    i would not pass this degree without you! an absolute gem

  • @gabrielladesch-obi5754
    @gabrielladesch-obi5754 5 років тому

    I have a calc final today and I had no idea what I was doing until rn thank u so incredibly much . When everyone has been sure I’d fail , I’d watch ur videos and turned up with some of the highest grades in the class . You r a life saver if I knew u and could pay you 1000 dollars I would but unfortunately I’m a poor student

  • @natashasthilaire1950
    @natashasthilaire1950 3 роки тому

    My calc final is later on today, thank you so much literally you are the only actual teacher I have

  • @V.Z.69
    @V.Z.69 4 роки тому +44

    I remember learning this. I got an 'A' in the class. An 'A' in Calc I, II, and III. Now, I just can't remember why I learned it and I never used it since I graduated.

    • @sooners2037
      @sooners2037 3 роки тому +2

      That happened to me when I was a undergrad barely used calculus until Atmospheric Dynamics decided to retake Calculus1-3 when I went to grad school occasionally I use Calculus but the computers do the calculations it’s good to know depending on the profession

    • @berkayustem6344
      @berkayustem6344 3 роки тому +7

      There's no such thing as A in Calculus

    • @iqrakhanamansari8670
      @iqrakhanamansari8670 3 роки тому

      Hey...is this 'TAYLOR SERIES' taught in clge or high schl??

    • @gnerdeek5362
      @gnerdeek5362 3 роки тому +1

      @@iqrakhanamansari8670 College. I'm pretty sure he meant college undergrad (the first few years of college, required for an associate's degree or bachelor's degree) vs college grad school (college to get a master's degree or doctorate).

  • @ningurp281
    @ningurp281 3 місяці тому +2

    I never did precalculus or calculus 1 and I understood this , wow... I didn't know what a factorial was and it is so fun..

  • @alejandroill
    @alejandroill 5 років тому +1

    Literally the most instructive math lesson I have EVER been given IN MY LIFE. Thank you so much

  • @jeremygalloway1348
    @jeremygalloway1348 3 роки тому

    Sir...you provide an immeasurable value to mathies everywhere. Of all creed, sex, sexual preference, race,and of all math levels.
    Those of us who are about to take our finals...SALUTE YOU!

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    @tejaamathi3039 3 роки тому

    I kind of wish that job interviews just conducted exams instead of making us waste our money to go to college to get a degree. I'm not an excellent test taker, but I'd much rather just self-learn and take an exam to get a job plus an interview session, rather than having to spend 40k+ on a degree. This channel just proves how one person can self-learn and be just as competent if not more competent than a person who studied for hours with a textbook. Thanks a million, OCT for helping me understand a topic in just 30min!

  • @homierdawg
    @homierdawg 3 роки тому +1

    God bless you Organic Chemistry Tutor. God bless you.

  • @biscuitquack9152
    @biscuitquack9152 2 роки тому

    This is my entire assignment sir. I can never thank you enough

  • @mwabakombe1238
    @mwabakombe1238 5 років тому

    You are a legend on your own ....I was like dreaming in class but when I opened the utube ....I found a lengend

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    @sandilemtambomalibongwe9477 3 роки тому +1

    You're the light shining every dark corners of the depart!!

  • @danimanabat5791
    @danimanabat5791 3 роки тому

    I hope you are living a blessed, happy life. Thank you for this!

  • @terrancepage9163
    @terrancepage9163 2 роки тому +1

    I'm at a point in my class where the textbook is zero help. I have no idea what its talking about anymore. This, however, is saving me and getting me through the class. Thank you so much!!!!

    • @terrancepage9163
      @terrancepage9163 Рік тому +1

      11 months later and I still have the same philosophy. Taking Differential Equations now and brushing up on my series knowledge. This is the video that just keeps on giving. You're a legend!

  • @ciiil8802
    @ciiil8802 Рік тому

    Passed my calculus thanks to this man.

  • @areebakhan5738
    @areebakhan5738 9 місяців тому

    this is perfect. watching your videos has helped me so much in university calculus!!!!!

  • @danytoumie1319
    @danytoumie1319 9 місяців тому

    YOU are the king of tutoring, thanks!

  • @danerasmussen2062
    @danerasmussen2062 2 роки тому +4

    I like how you always bring it back to that larger formula =, and you parse out what the series will be from there. It makes it very repeatable.

  • @adnanhowlader143
    @adnanhowlader143 4 роки тому

    while university taking my dad's hard working money and provides low level teaching , and you are sir doing god's work

    • @ethanwelling4546
      @ethanwelling4546 4 роки тому +1

      Just remember why you're doing this man.
      To get a goddamn piece of paper

  • @hannahdo980
    @hannahdo980 5 років тому +2

    Thank you so much! Didn't expect to understand Taylor and Maclaurin series this easily...

  • @wtfooqs
    @wtfooqs Рік тому

    your video got me to understand the concept more in 10 minutes than my university could in 2 hours. I FUCKING LOVE YOU, MAN.

  • @ArjunSinghBhadauriya
    @ArjunSinghBhadauriya 9 місяців тому +2

    Thank You for helping me for my exams.

  • @randomthinkingindividual
    @randomthinkingindividual 2 роки тому

    thank you very much! very helpful, studying at 2am for the tomorrow exam.. tired of reading the text so your video really helped

  • @endarkened5153
    @endarkened5153 3 роки тому

    It took me only 7 minutes to understand taylor and maclaurin series after watching 1 of your examples. Before that, I was scratching my head for 1 hour in class wondering what my professor was doing to get the taylor/maclaurin series.

  • @fatmacdacat
    @fatmacdacat 3 роки тому

    You are the only reason I have been passing my physics and calc classes. Many thanks. You down with OCT yeah you know me!

  • @tsadiamabel
    @tsadiamabel 4 роки тому +1

    Well done Sir. You are really a genius in Maths. All your explanations that I have watch are super-awesome. They are just so so so great. Words can't describe it. God bless you.

  • @nirmalupadhyay4548
    @nirmalupadhyay4548 Рік тому +1

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  • @emmafox7022
    @emmafox7022 6 років тому +6

    Thank you so much! Your videos really help me fill in the holes I missed in calculus originally.

    • @rajendramisir3530
      @rajendramisir3530 6 років тому

      Same here Emma. JG's majestic explanations and working through a variety of questions have excited my interest in Infinite Series. Utube was not there when I struggled with this topic. I didn't quite learned Combinatorics when I studied it. I am preparing to start the BS in applied and computational mathematics. We ought to support and subcribe to JG's Utube channel.

    • @almaktoumsajwani723
      @almaktoumsajwani723 4 роки тому +1

      Nice

  • @minhquangly8100
    @minhquangly8100 6 місяців тому

    Pay thoundsand of dollar and still going to this chanel for study. You desevered my tuition

  • @whoisdanielsong
    @whoisdanielsong 2 роки тому +1

    An incredible coverage of the Taylor and Maclaurin series. Great work

  • @Himawari_.
    @Himawari_. 6 років тому +2

    your way of teaching is really understandable sir. Thank you very much.

    • @zukauddin5327
      @zukauddin5327 5 років тому

      That was awesome, it has just cleared all the doubts I had regarding to single variable. I just want to ask that what if there will be two variables in the function

  • @themichaelcom
    @themichaelcom 6 років тому +4

    I really love your videos. I believe I got a 4.0 in chemistry because of you. Also because of my hard work, but you made it easier for me to achieve it. Thank you.

  • @bluestone1017
    @bluestone1017 6 місяців тому

    Sometimes i wish i could do your class face to face, you've been saving me, thankyou

  • @Trußþÿ_cŕuizè
    @Trußþÿ_cŕuizè Місяць тому

    Your work will be used forever!

  • @aarieffawwaz7984
    @aarieffawwaz7984 2 роки тому

    I HAVE A CALCLUS FINAL IN ABOUT 3 HOURS, I HOPE I PASS THIS COURSE. THANKYOUUU FOR THE EXPLANATION

  • @ΓιώργοςΜάριοςΜερκούρης

    This video is just pure mathematic gold! I

  • @georgesadler7830
    @georgesadler7830 Рік тому +1

    Professor Organic Chemistry Tutor, thank you for explaining the difference between Taylor and Maclaurin Series in Calculus Two. The two names that are most commonly associated with Power Series are Brook Taylor and Colin Maclaurin. Elementary and Transcendental Functions can be represented as Taylor/Maclaurin Series. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.

    • @poggom
      @poggom Рік тому

      what is this AI comment

  • @benjaminaboagye9846
    @benjaminaboagye9846 6 років тому +2

    WOW...You are an amazing tutor!!. God richly bless you

  • @aidengonzalez8073
    @aidengonzalez8073 6 років тому +1

    Thank you so much for this, lecture makes zero sense but I don't have to worry when I have these videos!

  • @11aanchalsharma48
    @11aanchalsharma48 5 років тому +1

    Best explanation ever of calculus

  • @qudusadewale1263
    @qudusadewale1263 4 роки тому

    You are amazing man. Please dont stop blessing us with knowledge

  • @rigelstar8037
    @rigelstar8037 4 роки тому

    I am in love with mathematics and you are great at teaching it my friend.

  • @alifarhat8072
    @alifarhat8072 5 років тому +6

    I stopped going to the sessions and prefer to go get my attendance in and leave class. Professor is useless, this is priceless!

  • @celsiusfahrenheit1176
    @celsiusfahrenheit1176 3 роки тому

    I don't care what people say, you are very intelligent

  • @swahilibrian7860
    @swahilibrian7860 4 роки тому +1

    If I could pay you i would...your methods are simple and easy to understand

  • @gleon1602
    @gleon1602 4 роки тому +1

    I understand Taylor and Maclaurin series thanks to you

  • @vhiedkc859
    @vhiedkc859 5 років тому +1

    🙏🏽🙏🏽. Better than the best
    From Tanzania.
    Asante sana

  • @minhvu8682
    @minhvu8682 4 роки тому +1

    Your lesson it's simple, easy to understand. Thank you so much.

  • @suhartiwijayanti1719
    @suhartiwijayanti1719 6 років тому

    all i can do to appriciate your video just not skip the ads

  • @lamiyanabaova3020
    @lamiyanabaova3020 3 роки тому

    You are real hero. It is not possible to describe my appreciation to you🌹

  • @Peter_1986
    @Peter_1986 Рік тому

    I literally watched this entire playlist from start to finish.