Power Series - Representation of Functions - Calculus 2

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  • เผยแพร่เมื่อ 28 ก.ย. 2024

ความคิดเห็น • 240

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  ปีที่แล้ว +12

    Final Exams and Video Playlists: www.video-tutor.net/
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    • @lightesque1407
      @lightesque1407 ปีที่แล้ว +1

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      @heath948 ปีที่แล้ว

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    @zeyaddessouki890 4 ปีที่แล้ว +659

    behind every successful student stands the organic Chemistry Tutor

  • @kylebledsoe1140
    @kylebledsoe1140 4 ปีที่แล้ว +140

    You just saved me! My calc 2 class went online and my textbook is extremely bare-bones and my teacher doesn't know how to do video lectures. Thank you so much for being so in-depth!

  • @Kokiriboy001
    @Kokiriboy001 5 ปีที่แล้ว +46

    I've been stressing over this stuff for the last 48 hours. My textbook and our math resource room was unable to help. You came to my rescue. I thank you sir!

  • @yonatandesta9680
    @yonatandesta9680 6 ปีที่แล้ว +601

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      @mintberry6014 6 ปีที่แล้ว +48

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      @Jeremy_Fisher 5 ปีที่แล้ว +45

      As soon as you barely feel comfortable with something, you get thrown back into the deep end, confused and scared.

    • @Lostwolf16
      @Lostwolf16 5 ปีที่แล้ว +2

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    • @Warwipf
      @Warwipf 4 ปีที่แล้ว +8

      Shoutout to all the German university students where, for some bizarre reason, calc1-3 is combined into Analysis 1, lol

    • @SmellyUnfortunate007
      @SmellyUnfortunate007 3 ปีที่แล้ว

      @Palpatine Welcome to mathematics, Senate. You are dealing in absolute.

  • @D1E4UG0
    @D1E4UG0 3 ปีที่แล้ว +7

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    • @TK-cb7ww
      @TK-cb7ww 4 วันที่ผ่านมา

      Did it?

  • @tinochigwada4652
    @tinochigwada4652 4 ปีที่แล้ว +2

    I have been using your videos since I was doing IGCSE O-level Cambridge examinations and now look at me in college still using your videos. I understand calculus 2 because of you! I know I'll be back on your youtube channel for calculus 3. You're my mathematical hero!! God Bless you * infinity!!

  • @MsSugarbunnies
    @MsSugarbunnies 4 ปีที่แล้ว +9

    This is such a blessing during COVID-19 times, especially since classes have been suspended. I can barely understand during class, and this is beyond helpful!! Thank you so much for your hard work and now I can pass my final tomorrow.

  • @dalisabe62
    @dalisabe62 2 ปีที่แล้ว +4

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  • @iphone6person21
    @iphone6person21 4 ปีที่แล้ว +3

    My god, thank you! Gotta love struggling in the hardest unit of the hardest calc class...

  • @COLLINSFENIN-rx6bo
    @COLLINSFENIN-rx6bo หลายเดือนก่อน

    Infact this man is a hero❤❤❤

  • @ssarpakai
    @ssarpakai 2 ปีที่แล้ว

    there is one thing to say about this video, 'LIFE SAVER.'

  • @celsiusfahrenheit1176
    @celsiusfahrenheit1176 3 ปีที่แล้ว

    Man, you're a lifesaver

  • @CLG111
    @CLG111 2 ปีที่แล้ว

    Ridiculously good video.

  • @anikatasnim8012
    @anikatasnim8012 4 ปีที่แล้ว +2

    you r a good man...

  • @abrarmahi
    @abrarmahi 4 ปีที่แล้ว

    if you were confused like I was (maybe I'm just stupid) . @ 5:04 r (lowercase) is the rate of the geometric sequence, and R (capital) is the radius of convergence.

  • @callummelrose7769
    @callummelrose7769 ปีที่แล้ว +1

    Thanks!

  • @SanDex-V-Felix
    @SanDex-V-Felix 4 ปีที่แล้ว

    U saved me ❤ i survived god bless u ❤❤❤

  • @jona4961
    @jona4961 ปีที่แล้ว +1

    His voice is nostalgic

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    @siahlwani8937 2 ปีที่แล้ว

    You saved my life

  • @enkancan
    @enkancan 4 ปีที่แล้ว +1

    You are my hero

  • @Clemfandang0
    @Clemfandang0 2 หลายเดือนก่อน

    My final is in 3 hours, wish me luck i will need it

  • @hamdymubarak3082
    @hamdymubarak3082 ปีที่แล้ว

    Are all power series representing a function have an open interval or do we have to test the endpoints in every problem?

  • @journeyriders7393
    @journeyriders7393 4 ปีที่แล้ว

    I think I need to buy a hoodie after all your intstruction masta

  • @spacee3249
    @spacee3249 ปีที่แล้ว

    If frustrated with classes, try speeding up to 1.25%

  • @angus8147
    @angus8147 4 ปีที่แล้ว

    Thank you so much ❤️感謝你

  • @pythonlearner2098
    @pythonlearner2098 4 ปีที่แล้ว

    In the last example can not I just use completing square in the denominator and solve it as the previous examples ?

  • @ummkulsumateeque3422
    @ummkulsumateeque3422 4 หลายเดือนก่อน

    I LOVE YOU!!!!

  • @nadavwolf6390
    @nadavwolf6390 4 หลายเดือนก่อน

    what if my denominator is something like (4x+1)^2?

  • @MicahTonning
    @MicahTonning 11 หลายเดือนก่อน

    Thank you!

  • @saugyanchapain7069
    @saugyanchapain7069 5 ปีที่แล้ว +1

    thank you

  • @SamuelLisita
    @SamuelLisita 5 หลายเดือนก่อน

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  • @davidcruz1469
    @davidcruz1469 ปีที่แล้ว

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  • @mauriceangly5598
    @mauriceangly5598 5 ปีที่แล้ว +2

    Also at 28:41, How do you come up with 3 as the center?

    • @ariel_alonso13
      @ariel_alonso13 5 ปีที่แล้ว +1

      thats what you are trying to find. its like if hes asking the question: "find the power series representation of the function: 8/2x-9 centered at x=3"

  • @imrankhawaja6751
    @imrankhawaja6751 6 ปีที่แล้ว

    Thank you sooo much!

  • @Thefakisgoinon
    @Thefakisgoinon 2 ปีที่แล้ว

    I have a function f(x)=1/(2-x) and i rewrite it as f(x)=1/(1-(x-1) which gives us a=1 and r=(x-1). However in my textbook it says that a=1/2 and r=(x/2)?

  • @nunoskid153
    @nunoskid153 10 หลายเดือนก่อน +1

    at 49:30 isnt the 1/x+2 negative?

  • @jamesm3828
    @jamesm3828 5 ปีที่แล้ว +12

    Why did I ever decide to take AP Calculus BC 😭

    • @michellemiao_
      @michellemiao_ 3 ปีที่แล้ว

      I ask myself this on a daily basis ughejfkdj

    • @gracehuynh7997
      @gracehuynh7997 3 ปีที่แล้ว +1

      @@michellemiao_ Ugh same this class is too much for my small brain T ^ T

  • @SamKuang-t7t
    @SamKuang-t7t ปีที่แล้ว

    Hi teacher, may I ask about one of the examples? 1/(3-x) can also be changed to 1/(1-(x-2)), so a=1, r=x-2
    But finally my answer is not the same as yours. The radius of convergence i found is 1, interval of convergence is (1,3).
    Am I missing any concepts ?

    • @minhluanne7462
      @minhluanne7462 ปีที่แล้ว

      'cause those of your result that depend on which value of c is given....

    • @jarenjenyik4743
      @jarenjenyik4743 4 หลายเดือนก่อน

      this is what I was thinking as well. I do not understand why this is not correct or if it isnt

  • @DVNreaction
    @DVNreaction 4 ปีที่แล้ว

    how can you be sure that |-x|

  • @christophernguyen8083
    @christophernguyen8083 ปีที่แล้ว

    22:00

  • @RebekahParkhurst
    @RebekahParkhurst 4 ปีที่แล้ว

    At 28:40: Why could you not first simplify by dividing through by 2? Then you'd have 4/(x-(9/2)) which completely changes the answer. Why does this not work?

    • @krystiangeldon7929
      @krystiangeldon7929 ปีที่แล้ว

      I know this is late but you would be changing the value of the equation.

  • @euler1
    @euler1 ปีที่แล้ว

    28:45

  • @abanoubnakhla9722
    @abanoubnakhla9722 ปีที่แล้ว

    Are you a doctor ? Cause all you do is save lives !

  • @anass26
    @anass26 5 หลายเดือนก่อน

    38:39

  • @mauriceangly5598
    @mauriceangly5598 5 ปีที่แล้ว +2

    Why do the two identical problems, one starting at 18:26 and one at 21:37 , start out identically but solve to difference radius s and different intervals???? They start out identical and you provide steps to reach 2 completely different answers???

    • @ariel_alonso13
      @ariel_alonso13 5 ปีที่แล้ว

      he centered the first one at 0, the second one was centered at 1

  • @jasmeherkathuria942
    @jasmeherkathuria942 5 ปีที่แล้ว +1

    In 8/(2x-9), why can't we just divide each term by 9 to get the 1 - r form? That method gives me an interval of -4.5 to 4.5. Is that the correct way to do it?

  • @benking2443
    @benking2443 ปีที่แล้ว

    CALCULUS 2 TATE 105 💯

  • @gabe7996
    @gabe7996 5 ปีที่แล้ว

    So what problems do you have to test the endpoints for?

  • @phuong-linhdinhm.2709
    @phuong-linhdinhm.2709 2 ปีที่แล้ว

    bro gud job!!

  • @redrom9270
    @redrom9270 5 ปีที่แล้ว

    I got a test tomorrow...ohhhhhhhhhhhhhhhh boy...

  • @AlpNavruz-eh7sf
    @AlpNavruz-eh7sf 3 หลายเดือนก่อน

    29:00😅

  • @tshepomashau3911
    @tshepomashau3911 5 หลายเดือนก่อน

    That one of 8/something it's wrong

  • @duckmancow1235
    @duckmancow1235 6 ปีที่แล้ว +1

    cool

  • @SamoanFor4everxx23
    @SamoanFor4everxx23 ปีที่แล้ว

    Those questions never come in the exam to be honest

  • @MarcusRangel704
    @MarcusRangel704 4 ปีที่แล้ว +1

    It’s 1am and my cal II final is at 7:30am. Wish me good luck by liking my comment lol

  • @shayanzandi6751
    @shayanzandi6751 ปีที่แล้ว +1

    I liked most of your videos but I absolutely hate this video of your's you made me so confused on this chapter. other explain it so much better.

  • @templetonpeck1084
    @templetonpeck1084 3 ปีที่แล้ว +3

    I did not like this video

  • @patrickas2057
    @patrickas2057 3 ปีที่แล้ว

    pog video

    • @MathElite
      @MathElite 3 ปีที่แล้ว

      I make a lot of calculus 2 videos on my channel please check them out.
      Appreciate any support

  • @ms.3124
    @ms.3124 4 ปีที่แล้ว

    can anybody help me with this one: (x+1)/(x+2)

  • @quoraexpert6295
    @quoraexpert6295 4 ปีที่แล้ว +1

    Idk about other ppl but I feel like Calc 2 is joke easy compared to calc 1

  • @conde3915
    @conde3915 4 ปีที่แล้ว

    I'm so low IQ lol i dont understand whats going on

  • @philipisibor6499
    @philipisibor6499 7 หลายเดือนก่อน

    In sum of powers series prove aₙ ➝ 0 please solve

  • @lorainesperling99
    @lorainesperling99 4 ปีที่แล้ว +397

    I have a feeling theses videos are about to blow up from all the students trying to get help for their online classes because of COVID-19

    • @mohamadelgendy4095
      @mohamadelgendy4095 4 ปีที่แล้ว +9

      Loraine Sperling here I am struggling to keep up wit my online class

    • @mryup6100
      @mryup6100 4 ปีที่แล้ว +1

      @@mohamadelgendy4095 lolol

    • @Yo-pn9qp
      @Yo-pn9qp 4 ปีที่แล้ว +12

      Isn't it wild we still pay full tuition? Smh

    • @Yo-pn9qp
      @Yo-pn9qp 4 ปีที่แล้ว +4

      God bless the everything tutor!

    • @shuaizeng4481
      @shuaizeng4481 3 ปีที่แล้ว

      can't agree more

  • @aileen5639
    @aileen5639 5 ปีที่แล้ว

    thank you!

  • @aayushpatel9768
    @aayushpatel9768 5 หลายเดือนก่อน +18

    watching 1 day before final exam

  • @Lefachie
    @Lefachie 6 ปีที่แล้ว +743

    you're a celebrity in my math class. we all talk about you, because we've all watched you. i was doing a problem on the board and my professor asked me if i watched "the organic chemistry turor" because she noticed that my notation was almost identical to yours. thanks man. i really appreciate your work

    • @JasonPwnsAll
      @JasonPwnsAll 5 ปีที่แล้ว +100

      does that mean ur prof watches too lol

    • @ahmetkarakartal9563
      @ahmetkarakartal9563 4 ปีที่แล้ว +16

      @@JasonPwnsAll ahhahaha

    • @BlackZephyrReal
      @BlackZephyrReal 3 ปีที่แล้ว +16

      We call him in our class "The Oct"

    • @SamuraiGuy
      @SamuraiGuy ปีที่แล้ว +3

      @@BlackZephyrReal we say "The O-Chem tutor".

  • @razabazal4669
    @razabazal4669 4 ปีที่แล้ว +199

    come on people just like two or three more sections to go then calc 2 is over we can do this!!! This is the hardest class i have taken so far without a doubt but it will all be over soon.

    • @nwshiar
      @nwshiar 4 ปีที่แล้ว +7

      AdvancedDynamicDisplacement Idk if you have or need to take calc based physic or not, but that’s gonna hit you like a train.

    • @razabazal4669
      @razabazal4669 4 ปีที่แล้ว

      @@nwshiar Do not need to fortunately I have heard that is wild

    • @tinochigwada4652
      @tinochigwada4652 4 ปีที่แล้ว +13

      Bless you for your comment. I am left with two weeks of school and believe me when I say your comment has given me so much encouragement!

    • @razabazal4669
      @razabazal4669 4 ปีที่แล้ว +8

      @@tinochigwada4652 that exactly why i posted it my brother everyone who comes here needs motivation

    • @Mar-eg3lk
      @Mar-eg3lk 4 ปีที่แล้ว +5

      try taking both together....

  • @sydneywest7197
    @sydneywest7197 5 ปีที่แล้ว +65

    I don't know if its the way you articulate each step over and over, even the smallest things, but I have studied your videos for a few hours and feel like I have genuinely studied this stuff for months. Its the way you set up your videos and subtly introduce nuances and slight difficulties so that when Im done I realize I have done all the problems with "tricks" and see how the concepts relate to each other. Truly brilliant.

    • @kvtys
      @kvtys 3 ปีที่แล้ว +2

      this comment ^

  • @devinmurphy6575
    @devinmurphy6575 3 ปีที่แล้ว +34

    Can we all just appreciate this man and his ability to save me on every single one of my calc tests. Explanations more clear than my actual Calc Professor

  • @xc4509
    @xc4509 5 ปีที่แล้ว +38

    Not gonna lie, I watch all your videos on 1.25x speed

    • @Lostwolf16
      @Lostwolf16 5 ปีที่แล้ว +6

      His speed is good for me

    • @pfeliciano4062
      @pfeliciano4062 4 ปีที่แล้ว +2

      His speed is perfect

    • @Gaby-fb7gh
      @Gaby-fb7gh 4 ปีที่แล้ว +1

      That's smart actually lol

    • @user-yr3uj6go8i
      @user-yr3uj6go8i 3 ปีที่แล้ว +3

      I watch his videos on 2x speed, lolz.

    • @saturnz428
      @saturnz428 3 ปีที่แล้ว

      For me it depends haha, if it is relatively easy I watch it in 2x but if it's challenging I watch it in 1.25x. His normal speed is too slow for me😂

  • @kimberlyheagerty547
    @kimberlyheagerty547 3 ปีที่แล้ว +20

    this man really knows how to do everything

  • @TheVirtualObserver
    @TheVirtualObserver 5 ปีที่แล้ว +59

    I have a fighting chance at my exam in a few hours because of your videos. Thank you SO MUCH for making these and for going over multiple examples of each type of problem in each vid. You're the best!! 😍

  • @bengrosskreuz2278
    @bengrosskreuz2278 6 ปีที่แล้ว +12

    I have an exam on this tommorrow and you didn't have these videos out at the beginning of the unit but you made them just in time!! Literally watching his videos makes everything so much easier to understand!!!!

  • @dulljumbo4321
    @dulljumbo4321 3 ปีที่แล้ว +4

    I dont care I just want a fucking formula i can pump my fucking numbers into and forget about this

  • @franksucro6765
    @franksucro6765 3 ปีที่แล้ว +7

    Honestly dude, thank you so much. Your videos literally help with anything. Some lectures just buzz through and don't truly get into need-to-know details. You make everything so simple and understandable.

  • @陈亦晨-d1p
    @陈亦晨-d1p 5 ปีที่แล้ว +9

    At 48:42, why it shows as 1/x+2 instead of -1/x+2 somehow?

    • @mateoortega719
      @mateoortega719 4 ปีที่แล้ว

      it's brought back at the end of the video

  • @Damian-vy8it
    @Damian-vy8it 5 หลายเดือนก่อน +1

    im not 100% sure but I think there is a mistake 20:00, when u factor 1/3 from the denomnator that should result in a 3/(1 - (x/3)) which the should turn into 3(x/3)^n which is x^n / 3^(n -1)

  • @rimmiekim
    @rimmiekim 5 ปีที่แล้ว +8

    God bless you, man 🙌🏼😭. you doing God’s work out here by helping us struggling students.

  • @dineshkumare1750
    @dineshkumare1750 ปีที่แล้ว +2

    Any one with exam tomorrow? (me)

  • @yona9257
    @yona9257 10 หลายเดือนก่อน +2

    for example number three why is it only x^3 and not -x^3
    for R

    • @thedarkdev3439
      @thedarkdev3439 9 หลายเดือนก่อน

      The formula is a / 1 - r; the negative in the " 1 - r " is part of it, so you would not include it. However, if it was, for example, a / 1- ( -r ) , you would include it as such.

  • @hesbonbaron4714
    @hesbonbaron4714 ปีที่แล้ว +1

    I wish our dear lecs could copy OCs method of content delivery.

  • @ryanlehning556
    @ryanlehning556 2 ปีที่แล้ว +1

    Im going to write in "The Organic Chemistry tutor" on the presidential ballot next time around.

  • @aSmelly1
    @aSmelly1 4 ปีที่แล้ว +8

    reviewing this for some higher level stuff that requires taylor series. At this point, I love math... but when he said partial fraction decomposition, I had some serious PTSD.

  • @drfrankphdboom9528
    @drfrankphdboom9528 4 ปีที่แล้ว +4

    Woah you teach everything from math to chemistry
    Damm
    Thanks a lot

  • @Xnibblet
    @Xnibblet 4 ปีที่แล้ว +4

    I think I've watched the majority of your videos. You are a master teacher over the web. Thank you so much for this and all other videos you do.

  • @spotsindude4045
    @spotsindude4045 5 ปีที่แล้ว +6

    Been watching this vid and slowly working along for the past 5 hours haha. Life of a math student. Thanks for these videos!

    • @Lostwolf16
      @Lostwolf16 5 ปีที่แล้ว

      Teaching yourself math looking up good videos like this is better way to learn and you learn more than in class

    • @mryup6100
      @mryup6100 4 ปีที่แล้ว +1

      Respect to you sir! 5 hours!

  • @kithenry
    @kithenry ปีที่แล้ว +2

    for the number at 21:27 , some one tell me why we dont use (1+2) as a replacement for three to make the function fit the GP template (a/(1-r))

    • @minhluanne7462
      @minhluanne7462 ปีที่แล้ว

      because we need to ensure that C value is=0 following the problem's request

  • @roebi5811
    @roebi5811 3 ปีที่แล้ว +2

    Awesome work JG! Just when I thought I conquered all algebra, it took Calculus 2 to teach me more algebra =)

  • @ahmetkarakartal9563
    @ahmetkarakartal9563 4 ปีที่แล้ว +3

    18:30 , why do we solve the problem by making 1 / (1-(x-2))? The answer becomes different than video's. Could you explain to me why it is different?

    • @mohanadnada4670
      @mohanadnada4670 4 ปีที่แล้ว

      3 is the same as 2 + 1
      so 1/3-x is the same as 1/2+1-x
      and since we want to represent the fn. in the form of 1/1-r
      so we will move the 2 next to the x so the fn. will be 1/1-x+2
      now a = 1 and r = (-x+2)

    • @michaelwhite1552
      @michaelwhite1552 4 ปีที่แล้ว +4

      @@mohanadnada4670 Ahmet clearly knows this (they have already broken it down to the same step you got to). Also, you forgot to factor out a -1 between your last 2 lines, so your r is off. The question is why does Ahmet get such a different looking power series by choosing r = (x-2), a = 1 than the video did. The long and short of it is that the two series, while looking very different, both will give the same results where there is convergence. By choosing r = (x-2), the series is centered at 2 with radius 1, so it only converges between 1 and 3. However, the solution provided in the video has a larger radius of convergence, spanning between -3 and 3. Therefore, the two different ways of writing the power series are not in fact the same; they only have equivalent infinite sums for x values between 1 and 3. You can verify this non-rigorously by plugging in a couple values of x within the radius of convergence for both series. They should be pretty close depending on how many terms you calculate out to.

    • @aakashSky-0
      @aakashSky-0 3 ปีที่แล้ว

      @@michaelwhite1552 thanks man, it was really helpful.

  • @nahushpethe1051
    @nahushpethe1051 2 หลายเดือนก่อน +1

    thank you bro

  • @yona9257
    @yona9257 10 หลายเดือนก่อน +1

    on the last example can someone explain why he wrote one over x plus two instead of -1 over x plus two

  • @21gamestreet
    @21gamestreet 4 ปีที่แล้ว +2

    at 30:30 was the negative factored out wrong or am I missing something?

  • @devkaneria8669
    @devkaneria8669 4 ปีที่แล้ว +2

    You are amazing ! Got my exam in couple of days and i'm really confident about it because of your videos! The stuffs my profs teach in couple 3-4 hours you teach it in less than an hour.

  • @sedonadettwiler8127
    @sedonadettwiler8127 2 ปีที่แล้ว +1

    Clarification Question: at about 43:30 you say that r is -x/2. does the x^3 in the numerator of the original function not impact what r is? is r the same for both x^3/x+2 and 1/x+2?

  • @cr7neymar908
    @cr7neymar908 10 หลายเดือนก่อน +1

    This is easily the hardest part of calc 2. Thank god I did good in the other chapters so my grade can afford it

  • @nyunai298
    @nyunai298 3 ปีที่แล้ว +1

    Excellent. I Feel like I'm ready for the mathematics olympiad

  • @someone26771
    @someone26771 7 หลายเดือนก่อน

    Hello please when you make it next time please be quick because we have lots of things to do after the video 😢😢😢 please

  • @yungfella745
    @yungfella745 ปีที่แล้ว +1

    goat

  • @arekkrolak6320
    @arekkrolak6320 4 ปีที่แล้ว +1

    this is all good material, but now how do you deal with functions like sin(x)? :)