Finding Power Series by Differentiation - 3 examples

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  • Опубликовано: 9 янв 2025

Комментарии • 109

  • @BloodlessSalvation
    @BloodlessSalvation 10 лет назад +215

    When you apologize for a long video, you realize this 13 minute video helped me more than reading and staring at the textbook for 2 hours and trying to figure out why I have to multiply by a half to the series on part b.

    • @marcusj.merritt6862
      @marcusj.merritt6862 10 лет назад +4

      I admittedly do the same thing with my calc book everyday as well. [facepalm]

    • @zuhrymousa12345
      @zuhrymousa12345 9 лет назад

      KimichiSushi 100% true!

    • @ExecrationZero
      @ExecrationZero 8 лет назад

      +KimichiSushi People learn differently.

    • @Nixiliog
      @Nixiliog 6 лет назад

      can't be anymore truer. Why do textbooks have to be written like darn hieroglyphics T_T

  • @brucelee570
    @brucelee570 7 лет назад +55

    I think you've helped raise the collective gpa of calculus students more than the infinite sum of 1/n

  • @lorib285
    @lorib285 8 лет назад +21

    GAACK!!! This stuff takes some intuition I just don't have yet! Keep this up please so I'll have a prayer!

  • @mollydenton6724
    @mollydenton6724 6 лет назад +1

    Was panicking all day because I have a quiz over this tomorrow and havent been able to figure it out. You truly rock my dude

  • @2ttaher253
    @2ttaher253 10 лет назад +9

    I`m student in ksa in FBSU
    Your lessons and Your style of the callouts lessons very useful and wonderful
    I benefited from your lessons of two years
    thank you so much
    keep going

  • @anamattson4442
    @anamattson4442 6 лет назад

    I have been confused for weeks, happened upon this video, and now get it! Thank you much.

  • @IIOXIDIZEII
    @IIOXIDIZEII 9 лет назад

    VERY helpful pat, 8:03 made me giggle. LOVE all your tricks and "what if" situations, they are thoroughly explained which help understand EVERYTHING!

  • @jjrimz99tandem_drifter
    @jjrimz99tandem_drifter 9 лет назад +1

    in the 12 minutes i have watched this video, it took my teacher 2 hours. Mad props!

  • @dhbballer16
    @dhbballer16 11 лет назад

    Wow I could not for the life of me understand how to differentiate a function when given a known series... This was a life saver! Thanks so much:)

  • @congcongai8081
    @congcongai8081 Год назад

    Your video explained everything well better than my college calculus teacher did.

  • @bobbytrap2554
    @bobbytrap2554 6 лет назад +1

    I love how this is the exact example I was stuck on, thanks!

  • @ghostfrom1950
    @ghostfrom1950 3 года назад

    I love it when math tutorial videos say they're trying not to let the video go for too long. Meanwhile, that's what some of us want! That's the glory of RUclips, if someone is in a real hury, they can either speed up the video or scrub thru. The skip forward shortkey is "L", which is no problem at all. MAKE THEM LONG! As long as the video stays on topic, I want to learn damn it!!!

  • @ricaulcastellon9615
    @ricaulcastellon9615 4 года назад

    Crystal clear, very well explained. You are the best!

  • @CouldUseARide
    @CouldUseARide 8 лет назад +11

    Got my final exam in 3 days. Thanks a lot!

  • @lexengland6443
    @lexengland6443 3 года назад

    Thank you so much! This explanation was super clear I’ve been having a really hard time with this topic and now I understand.

  • @brehbrehgentil
    @brehbrehgentil 11 лет назад

    you are my hero, the index subtlety had bent my mind. thx u 4 unbending

  • @Katie75522
    @Katie75522 9 лет назад +58

    U r my savior, Patrick. If I ever see you one day on the street, expect a high-five 4-sure

    • @vivaldikonzsmith7291
      @vivaldikonzsmith7291 7 лет назад +2

      He actually expects a little appreciation with some dollars, I am pretty sure your high five dont pay bills.

  • @s.alizapiotrowski1474
    @s.alizapiotrowski1474 6 лет назад

    Thank you so much, Patrick! I am studying Complex Analysis and reviewing Series. This is very helpful!

  • @allisonm4998
    @allisonm4998 8 лет назад +25

    You're my favorite.

  • @aimaladil6564
    @aimaladil6564 5 лет назад

    Assalam o Alaikum....patrick....really helpful in exams...stay blessed...from Pakistan

  • @cakkuncaktinmilo4032
    @cakkuncaktinmilo4032 11 лет назад

    u just save my day patrick..thank you very much

  • @cediemacalisang7713
    @cediemacalisang7713 8 лет назад +1

    You explain very clearly.

  • @MrHelpingHand
    @MrHelpingHand 7 лет назад

    Great video man! Thanks for all of the help!

  • @hengstar
    @hengstar 10 лет назад

    Very nice, man. Thanks for saving me from struggling

  • @fcortesjp
    @fcortesjp 9 лет назад +6

    on c) if i leave the index equal to 0 and not compensate for the shifting shouldnt that be ok since you are still getting 0's for first two values in the series when n=1 and n=0 ?

    • @Mary-mj7le
      @Mary-mj7le 5 лет назад +2

      well i guess we'll never know

    • @CarsonJamesCook
      @CarsonJamesCook 3 года назад

      I agree, for whatever that's worth (6 years later...).

  • @MrMultiMacedo
    @MrMultiMacedo 6 лет назад

    you saved my life thank you so much

  • @idbaronco4194
    @idbaronco4194 7 лет назад +3

    Me has salvado amigo! muy buen vídeo, aunque no sepa hablar ingles te entendí perfectamente gracias a tu paso a paso bien explicito

  • @mistacoward7761
    @mistacoward7761 8 лет назад

    That video was outstanding.

  • @Vampirekat123
    @Vampirekat123 8 лет назад +3

    How would the expression change if the function is f(x) = (6-x)^-4. or any other power that is lower than -3?

  • @bayanashoori
    @bayanashoori 6 лет назад

    *You bring nothing but honour to your family*

  • @cardinaltutor5711
    @cardinaltutor5711 5 лет назад

    Thank you. This video helps me a lot.

  • @reaniegane
    @reaniegane 7 лет назад

    When you apologized for the length of your video, I was just hoping that your video would go on because it is so good.

  • @zo5796
    @zo5796 11 лет назад

    Thanks so much, definitely subscribing!

  • @sapphire9724
    @sapphire9724 6 лет назад

    BLESS YOU PATRICK

  • @miguelmanturano9108
    @miguelmanturano9108 10 лет назад +2

    Thank you for taking your time to make this video.(:) )

  • @FlashFire40
    @FlashFire40 12 лет назад

    Hey, this almost exactly matches the book problem I just did. The only difference is that in my problem, a) was 1/(1+x)^2. Otherwise, exactly the same. So this is perfect. And yes, I also have the book Single Variable Calculus: Early Transcedentals.

  • @xlGotStridelx
    @xlGotStridelx 9 лет назад +4

    This is a great video, now if only you could use functions that didn't have a (1+x) in the denominator and instead had something like (10+x), that would be very helpful!

    • @1hit2hitown
      @1hit2hitown 8 лет назад +9

      +Martin Velarde all you have to do is factor out a 10 then you would be left with 10( 1+x/10) and continue as in this video.

  • @reubenwilliammpembe667
    @reubenwilliammpembe667 6 лет назад

    You are the best!!! Thank you so much

  • @rohith5062
    @rohith5062 7 месяцев назад

    2:25 why cant i just divide by (1+x)^2 to get series sum for 1/(1+x)^3

  • @WifeSoup2
    @WifeSoup2 12 лет назад

    Literally amazing.

  • @adammann6582
    @adammann6582 9 лет назад

    a perfect math video 🙌 .than you Patrick

  • @Rxpeme123
    @Rxpeme123 8 лет назад +1

    I was wondering if you could help answer a question that I'm having a really hard time with. It asks to find the derivative of the summation from n=0 to infinity of (-1)^nx^(2n+1) / 3^(2n)(n!)^2. I have no idea how to solve this, your help would be greatly appreciated :)

  • @Bobboboll97
    @Bobboboll97 8 лет назад

    Thank you, this helped me a lot!

  • @rachellee3050
    @rachellee3050 4 года назад

    your handwriting is good

  • @nmpopa
    @nmpopa 11 лет назад +1

    Is it necessary to change the index from the second series in order to compute the third one?

  • @Daiz7788
    @Daiz7788 7 лет назад +1

    Do you have to change the n from n=0 to n=2 or can you leave it as n=0?

  • @TheBikhinkl
    @TheBikhinkl 11 лет назад

    I hope I will have a Calc teacher as good as you in college this fall. otherwise, my calc future will be bleak as in HS...

  • @coryfreestyle
    @coryfreestyle 9 лет назад

    Thanks, you are the best!

  • @jdilley00
    @jdilley00 13 лет назад

    Patrick. Do you cull alot of your examples from the textbook "Single Variable Calculus: Early Transcedentals"? Alot of your examples match up =)

  • @6norcal9
    @6norcal9 12 лет назад

    Patrick the book gives a solution to 1/(1+x)^2 to be the series from n=0 to infinity of (-1)^n*(n+1)*x^n, this differs from what you have, if you could please explain the difference it would be of great help. Thanks!

  • @yasothar4976
    @yasothar4976 9 лет назад

    If you dont change the index in part b (where it still remains from n=0 to infinity ) , would it affect your final answer ?

  • @katherineweinzierl586
    @katherineweinzierl586 5 лет назад

    I'm confused as to how you got the part after the sigma. I'm trying to follow this and solve a different equation with the steps you use but I can't seem to figure out how to get the (-1)^n(n)(n-1)x^(n-2) or (-1)^n(n)x^(n-1) parts???

  • @that1guywhoknows
    @that1guywhoknows 11 лет назад

    If my calc teacher didn't point you out, I'd be failing

  • @mollyc2575
    @mollyc2575 7 лет назад

    Question. Would it be alright if I careless about the change of n=0 to n=2, and then comd back to n=0 ?

  • @guiguspi
    @guiguspi 8 лет назад +1

    Thx for the content.

  • @rylanchinnock4871
    @rylanchinnock4871 8 лет назад

    This is great!

  • @toddj.2
    @toddj.2 6 лет назад

    Patrick, as a convention, can't we just increase a (the lower bound) by 1 every time we differentiate? That may be a more efficient approach, no?

  • @berfin2523
    @berfin2523 4 года назад

    for b, if you initialize it from 0 then it will be same with c?

  • @Kitkat915e
    @Kitkat915e 8 лет назад

    Just a question: how would you use these derivative versions to find the radius of convergence? Or would the radius be unchanged?

    • @bryancabrera2702
      @bryancabrera2702 7 лет назад

      Kitkat915e I may be a little late, but the radius of convergence would in fact remain unchanged. However, the interval of convergence could change.

    • @Kitkat915e
      @Kitkat915e 7 лет назад

      Oh, thank you :)

  • @xen05z
    @xen05z 9 лет назад

    3:40 no you can't leave it 0 because the stupid WebAssign homework grader will keep saying you're wrong. So you have to make n = 1, once you get you sum formula, change n to 0 and add 1 to all n's in your formula. I don't know, but that;s what WebAssign wants...

    • @xen05z
      @xen05z 9 лет назад

      WebAssign and MasteringPhysics.

  • @Sdollas
    @Sdollas 8 лет назад +2

    WHY WASNT N=1
    N=1 WHEN YOU DID AN EXAMPLE IN THE PAST, WHICH IS AFTER YOU TAKE THE DERIVATIVE OF THE SERIES

  • @AteenJoy13
    @AteenJoy13 11 лет назад

    My calc teacher sucks, thanks patrick

  • @perryleigh9028
    @perryleigh9028 11 лет назад +1

    How did you get the sum from n=1 to infinity of ((-1)^n)(n)(x^(n-1) my textbook got (-1)^n(n+1)x^n

  • @Ftom14cat
    @Ftom14cat 12 лет назад

    hey patrick, this video is not included in your calc 2 playlist and it seems like it should be

  • @GodOfJazzDylan
    @GodOfJazzDylan 11 лет назад

    That's great, but how do you do it when it isn't (x+1)
    What you have shown is easy, but I have no idea to do it with, say, 1/(1+5x)^2 or x^2/(7+x)^3

  • @loatilelebala6749
    @loatilelebala6749 3 года назад

    THE GOATTTTT

  • @williama.3193
    @williama.3193 10 лет назад

    8:13 is there an add on? lol

  • @felixsamuel9714
    @felixsamuel9714 7 лет назад +1

    legend

  • @moozchi3
    @moozchi3 10 лет назад

    hi patricjmt! can you please do 3 more examples for power series representation using differentiation and integration? THANK-yOU!!!!

  • @byJayzik
    @byJayzik 7 лет назад

    Radius of convergence?

  • @Misstewee
    @Misstewee 9 лет назад

    Thank you thank you thank you!!!!

  • @lilliflower743
    @lilliflower743 10 лет назад

    Thank you!

  • @skategenie
    @skategenie 11 лет назад

    I can smell his sharpie from here!

  • @Jayson8888
    @Jayson8888 3 года назад

    shoutout pat

  • @that1guywhoknows
    @that1guywhoknows 11 лет назад

    I believe you try to get it into the form 1/(1-x)

  • @anoniem012
    @anoniem012 6 лет назад

    Thank you !

  • @kylemorris371
    @kylemorris371 8 лет назад

    isn't that the taylor series? the taylor series is only for a_n(x-c)^n

  • @DonPasquale_
    @DonPasquale_ 7 лет назад

    I know this video is super old but does anyone know what to do if you have 1/(1+x^4)^(3/2)?

  • @leohe2690
    @leohe2690 5 лет назад

    Really should have watched your videos earlier.. Now it is only little time before my exam...

  • @KMBillah
    @KMBillah 11 лет назад

    Why the calculus teachers don't watch these videos ? i mean they can learn the teaching !

  • @SlowKlone
    @SlowKlone 5 лет назад

    probably the hardest thing in calc 2 is this, im completely lost

  • @brendanbramman
    @brendanbramman 11 лет назад

    Why do you keep changing how you write your twos!! It bothers me so! Great video by the way, thanks.

  • @brucelee7150
    @brucelee7150 11 лет назад +1

    idk why but i keep losing him in this video

  • @mehmetkurucu18
    @mehmetkurucu18 6 лет назад

    2018?

  • @peeweewoen
    @peeweewoen 11 лет назад

    then u haf to differentiate or integrate it...look at his other video

  • @johnperez3
    @johnperez3 8 лет назад

    you forgot to derive.....

  • @poifquackula6665
    @poifquackula6665 6 лет назад +1

    OMFFFGGGG so annoying! Please normalize the audio of your video before uploading so I don't have to turn the volume of my computer all the way up in order to hear you

  • @logoscafe
    @logoscafe 11 лет назад

  • @fernandoalejo
    @fernandoalejo Год назад

    I hate power series

  • @joeldevries2981
    @joeldevries2981 10 лет назад

    Thank you!

  • @AstreaChanellMen
    @AstreaChanellMen 5 лет назад