Direct Comparison Test - Calculus 2

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  • Опубліковано 11 січ 2025

КОМЕНТАРІ • 265

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +17

    Next Video: ua-cam.com/video/LBxYQ0TJxYM/v-deo.html
    Final Exams and Video Playlists: www.video-tutor.net/

    • @Idurangalk
      @Idurangalk Рік тому

      Isn't 1/n convergent

    • @audiomac
      @audiomac Рік тому

      @@Idurangalk 1/n is convergent, but its series is not. Look up p-series to look up more on the topic.

    • @MukyalaDoreen
      @MukyalaDoreen Рік тому

  • @joshuaway
    @joshuaway 9 місяців тому +100

    My man is carrying the entirety of the next generation's higher education on his shoulders

  • @ParthMaitreymarvel
    @ParthMaitreymarvel 6 років тому +470

    The most underrated channel

    • @tabtibelkacem2824
      @tabtibelkacem2824 6 років тому +3

      ikr

    • @mryup6100
      @mryup6100 4 роки тому +2

      @Txawjntse Vang wuzzy

    • @Purpose_Porpoise
      @Purpose_Porpoise 4 роки тому +2

      @Txawjntse Vang lol I was not expecting that reply so I actually laughed.

    • @janedoes5903
      @janedoes5903 4 роки тому +12

      Lmao he has over 2 million subscribers. Most don't take calculus and many avoid it at all costs.

    • @elder7241
      @elder7241 2 роки тому +2

      not anymore lmao

  • @aunpaidintern7035
    @aunpaidintern7035 5 років тому +494

    I cannot thank you enough! I'm a full time college student living out on his own in an apartment so I work nights from 10PM-6AM five times a week and sometimes miss out on info during lectures. This section has been brutal to me.

  • @Oscar-gx2yf
    @Oscar-gx2yf 5 років тому +139

    Do you realize what a huge help you are to so many people!? You deserve more attention! Thanks for all the videos you make you are my favorite youtube instructor of all time hands down!

  • @rmdir
    @rmdir 2 роки тому +149

    An analogy.
    You are driving home in your car with a friend. The car is low on gas, the low gas light comes on.
    Your friend lives a few miles before your house, on the way, less distance.
    If you make it home (converge) of course so did your friend.
    But if your friend makes it home, that doesn't mean you won't run out of gas on the way to your house (diverge).
    Same situation here.

    • @AM-fh5rx
      @AM-fh5rx 2 роки тому +10

      what a nice way to explain it thanks man

    • @ziaddd6919
      @ziaddd6919 Рік тому +8

      thanks for this, my professor was so confusing when he explained it

    • @MeinCouch123
      @MeinCouch123 Рік тому +4

      Very very nice way to put it 👍

    • @Silenwrld
      @Silenwrld Рік тому +2

      That's deep man😊

    • @Silenwrld
      @Silenwrld Рік тому +2

      10:34

  • @juanls4643
    @juanls4643 6 років тому +128

    you and patrickjmt are the people i pray to thank you everynight

    • @bicboi46
      @bicboi46 6 років тому +25

      Honestly though man. The internet is a beautiful thing, i honestly feel bad for people that struggled in math before the internet was a thing.

    • @umeramjad8692
      @umeramjad8692 4 роки тому

      Sameee ☺️☺️☺️

    • @roseayoro9158
      @roseayoro9158 4 роки тому

      @@bicboi46 its just something dope doing math

  • @claireeckhardt4472
    @claireeckhardt4472 Рік тому +20

    Hi! Just wanted to let you know that your channel has been extremely helpful recently!! My calculus teacher passed away in January, and she was one of the best teachers I’ve ever had. I know she would have wanted me to continue working hard in her class, so I’m doing the best I can with your videos and a new teacher. Thanks for all you do!!!

    • @brokescholar
      @brokescholar Рік тому +3

      Hey, good luck and don’t give up! RIP to your awesome calc teacher

  • @pfeliciano4062
    @pfeliciano4062 5 років тому +6

    The problem at 11:50ish is true guys because remember we have been given a restriction if n is greater than or equal to 3. So if you were to plug in 3 you can actually see that 1/n is smaller.
    Also keep in mind that you need to simplify for the second to last problem n/n^2 becomes 1/n

  • @darwinorsler3881
    @darwinorsler3881 Рік тому +3

    You are just awesome. Consistently through the past year, whenever I've struggled to understand a concept or technique, your videos make it click.

  • @terrancepage9163
    @terrancepage9163 2 роки тому +7

    that graph visual really helped me understand things so much clearer! thank you!!!

  • @RamytRamyt
    @RamytRamyt 6 років тому +7

    I can't believe I only now found your videos. They are SO helpful, and make these problems so much easier to understand. Thank you!!!!

  • @safaalqaysi8612
    @safaalqaysi8612 5 років тому +43

    I get so sad whenever he says "This is the last example for this video''

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    @michellemathew_ximb6286 6 років тому +15

    you're a life saver, thank you so much 😭❤

  • @elguis201109
    @elguis201109 5 років тому +8

    I can always count on this channel for the 2am next day exam cram

  • @slowpr0
    @slowpr0 6 років тому +6

    I don't even have to go to class, I just watch your videos before my quizzes. Good stuff man

  • @Dwills-cp8wr
    @Dwills-cp8wr Місяць тому

    Best math channel, been watching a lot of your videos, they are a lot of help. Thank you!

  • @helpontheway7856
    @helpontheway7856 6 років тому +6

    Thank you for doing these!
    If you can, please do one on Taylor and Maclaurin series & Power series.
    Exam Monday and you’ve helped me ace everything

  • @LongRangeBacon
    @LongRangeBacon 5 років тому +3

    excellent video. I feel twice as ready for my exam tomorrow.

  • @el_jvy4
    @el_jvy4 11 місяців тому

    honestly my best teacher on youtube

  • @fatmacdacat
    @fatmacdacat 3 роки тому +3

    OCT...I hands down, absolutely, without a doubt, attribute every passing grade in my math and science classes to you! Thank you OCT! You down with OCT yeah you know me!

  • @celineguler
    @celineguler Рік тому +2

    8:56 why inconclusive? we didn't check a smaller series but by just a bigger series is divergent we say it's inconclusive?

    • @cortiz8726
      @cortiz8726 Рік тому

      what else is there to check? You use limit comparison test if you get inconclusive

  • @annpham6455
    @annpham6455 5 років тому +2

    u r a math god, thank u for humbly serenading us w ur godtier wisdom

  • @clutchmadness
    @clutchmadness 5 років тому +10

    @11:44, I don't understand how he arrived at 1/n. Can someone please explain? All in all, it's still a great video :)

    • @mryup6100
      @mryup6100 4 роки тому

      because the numerator becomes insignificant compared to the denominatoe?

  • @masheroomboi2884
    @masheroomboi2884 Місяць тому

    this man can deadlift an entire graduating class

  • @hayley863
    @hayley863 5 років тому +1

    As an engineering student at Purdue, may you be blessed in all facets of life. We love you.

    • @rockyk6805
      @rockyk6805 5 років тому

      How is Purdue for engineering?
      I was thinking of transferring

    • @hayley863
      @hayley863 5 років тому

      @@rockyk6805 As far as rankings go, it's 7th in the US. Classes are pretty rigorous, but there are a lot of supplemental resources available, and if you do well and get your degree, you can basically count on landing a good job after graduation. Not to mention that it's a leading research university, which opens up a lot of opportunities for undergrad experience. On a more personal level, I do love the school. The people are chill, most of the professors are great (excluding some for the weed-out classes), and it's overall a solid choice.

    • @rockyk6805
      @rockyk6805 5 років тому

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    • @vipari
      @vipari 9 місяців тому

      @@hayley863You graduate?

    • @hayley863
      @hayley863 9 місяців тому +1

      @@vipari I did, but from a different school. I actually ended up transferring to a school in my home state :)

  • @TMAJ0R
    @TMAJ0R 2 роки тому +1

    Remember if An=< Bn it will converge unless An goes to negative infinity

  • @janedoes5903
    @janedoes5903 4 роки тому +2

    I made it to calc 2 and I'm so happy.

  • @maktub_txt
    @maktub_txt 4 роки тому +2

    I have my calculus 2 exam tomorrow and i literally cried because i couldn't understand these.Watching these 9 hours before the exam and man i just wanna say thankyou Allah apki dunya aur akhrat achi karey

    • @Giblet12
      @Giblet12 4 роки тому +1

      Haha same boat here. Exam is in 21 hours for me

    • @maktub_txt
      @maktub_txt 4 роки тому +2

      @@Giblet12 *cries in calculus*
      Best of luck ✨

    • @Giblet12
      @Giblet12 4 роки тому

      @@maktub_txt Thanks my man

  • @nug700
    @nug700 6 місяців тому

    I always watch this guys videos before the lectures by my professors... always.

  • @aevaristus2410
    @aevaristus2410 3 роки тому

    The savior of my calc grade

  • @onur7192
    @onur7192 6 років тому +5

    thanks my teacher you're a good teacheer

  • @rambhayadav9854
    @rambhayadav9854 3 роки тому +1

    Thanks a lot sir 👍. I got cleared the concept of direct comparison test . I wasn't knowing it so clearly .

  • @narayanthapa4361
    @narayanthapa4361 4 роки тому

    I love you ❤ you are awesome i had wasted 4hrs trying to understand this you made me understand this in 15 mins.🥺🥺🥺 love you

  • @egetahhan298
    @egetahhan298 6 років тому +1

    You saved my life mann great presentation

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    @lhbkjfymbf 5 років тому +1

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  • @emftka1
    @emftka1 6 років тому +12

    It really helps , even though I don’t know english

    • @onurucar1112
      @onurucar1112 4 роки тому

      it's another moment of when foreigners say they don't know english but speak way better than the natives.... respect

  • @hristinamiljkovic1392
    @hristinamiljkovic1392 6 років тому +2

    I LOVE YOU SO MUCH thank you for all the videos!!!

  • @camileclere8925
    @camileclere8925 3 роки тому

    you're so good at teaching

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    @fourn7wenty 4 роки тому

    I bet you never thought how important your channel would be

  • @hokagesama758
    @hokagesama758 5 років тому +3

    he's gonna save my semester yehe ; -- ;

  • @mertovski8793
    @mertovski8793 5 років тому +1

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    @andrewbarney5245 4 роки тому +2

    LITERALLY SAVING MY LIFE

  • @Sultan-le8so
    @Sultan-le8so 4 роки тому +1

    You are the best, that all what I can say, thank you my legend ❤️

  • @kulsumkader9410
    @kulsumkader9410 3 роки тому

    Thanks a lot for saving my calc grades

  • @hannanbaig7888
    @hannanbaig7888 5 років тому +1

    at 11:53 why didnt you consider ln(n) / n (the bigger series) instead of 1 / n (the smaller series)?

    • @pfeliciano4062
      @pfeliciano4062 5 років тому

      Hannan Baig yeah I was confused, because if you were to plug in any number the bigger one would be 1/n

    • @pfeliciano4062
      @pfeliciano4062 5 років тому

      Oh I figured it’s because we had a restriction of n is greater than or equal to 3

  • @InayatKhan-xx8in
    @InayatKhan-xx8in 5 років тому +1

    Most concept full channel

  • @RealPixelFusion
    @RealPixelFusion 2 місяці тому

    I have a question about the graph at 2:20, if the sequence itself is converging but it’s converging to a number above 0 then the series will be divergent , then all the graphs he drew should be divergent?

  • @juanjo984184333
    @juanjo984184333 3 роки тому

    Thanks is most useful your video than others.

  • @nvn7291
    @nvn7291 2 місяці тому

    These vids always help me better understand concepts I don't always understand right away in class. Can you do more examples with trig though? I always feel so confident breezing through the first questions in my textbook but once I get to the problems with lots of trig it's an uphill battle.

  • @dimnaprado7764
    @dimnaprado7764 4 роки тому +1

    These videos are so helpful!! Thank you!

  • @bettkiprono9855
    @bettkiprono9855 3 місяці тому

    What a wonderful lesson. Keep it up.

  • @adabujiki
    @adabujiki 4 роки тому +1

    hmm.... thanks dude-- i read the book for weeks but they never tell you how the original function 1/2+3^n became 1/3^n and 1/2+3^n | so thanks for using the big function small function analogy.

  • @tatiaa7206
    @tatiaa7206 5 років тому +25

    when will he do a face reveal. I've been watching his videos for 2 years and I need to know how he looks like.

  • @audiomac
    @audiomac Рік тому +1

    The section at 11:15 was explained poorly. The point he was trying to make was ln(n) is greater than 1/n once n is > or equal to 3 SINCE ln(n) will THEN be greater than 1/n's numerator, which is simply 1.

    • @rohhanbhardwaj
      @rohhanbhardwaj 10 місяців тому +1

      thanks

    • @audiomac
      @audiomac 10 місяців тому +1

      @@rohhanbhardwaj I’m glad my comment helped someone 😁😁

  • @zekebranham9997
    @zekebranham9997 3 роки тому +1

    Amazing explaination

  • @fathimarishna4075
    @fathimarishna4075 3 роки тому

    I follow your all the vedios🌝 🥺🥺 again thank you🥺❤😍😘

  • @stephenchanda7580
    @stephenchanda7580 6 років тому

    Thanks a lot. I'm liking the new colors. It looks great

  • @fathimarishna4075
    @fathimarishna4075 3 роки тому +1

    More more more more...🙏 thank you😍🥺😘😘

  • @reidgarrison9629
    @reidgarrison9629 2 роки тому

    10:55 why cant we use L'hospital rule when n goes to infinity wouldnt the bid series go to zero ?

  • @azxcv83
    @azxcv83 6 років тому +1

    Thanks man.You are a life saver

  • @JoeyFinianos
    @JoeyFinianos Рік тому

    best content ever very usefull thank you for everything

  • @YasmineTajeddin
    @YasmineTajeddin Рік тому

    Thank you this was really good and helpful!!!!

  • @amankikani4354
    @amankikani4354 Рік тому

    I don't know why but 8:35 sounds like the perfect time for some V-sauce music

  • @alexisazuara9649
    @alexisazuara9649 3 роки тому

    I would be proud to shake this mans hand

  • @melvinjohn5023
    @melvinjohn5023 4 роки тому

    Superbb keep making 👍👍👍👍👍👍👍

  • @MeRcuRy6699
    @MeRcuRy6699 5 років тому +1

    Omg thank you very much bro. You helped me

  • @johnperez3454
    @johnperez3454 Рік тому

    At 12:10 why is it allowed to do n >= 3 I thought all Bn terms had to be bigger than An terms. Is it because they are only 2 terms that dont follow that which doesnt affect the whole series because only 2 terms affecting a series of infinite terms is very small relative to it.

  • @learninghome5396
    @learninghome5396 5 років тому

    The examples are very simple!!!

  • @zarkmuckerberg8341
    @zarkmuckerberg8341 3 роки тому +1

    Can anybody explain how he got convergence at 5:06? I thought that n

    • @squidcurry9955
      @squidcurry9955 3 роки тому +1

      you're probably thinking of the p series test, what he did there was a geometric series

    • @mahamadmarshall9031
      @mahamadmarshall9031 2 місяці тому

      Bro u think of p series

  • @maxdegreat566
    @maxdegreat566 3 роки тому

    in class i was lost, on hawks i was confused on yt it all makes sense lol thanks

  • @ahmadabdel9114
    @ahmadabdel9114 5 років тому

    Thank you very much, I hope you keep going up to diff

  • @minkihairoil
    @minkihairoil 3 роки тому

    for 7:59 wouldn't the first one be greater than or equal to the second? Since you're dropping the 4 that one would be smaller no?

    • @davidzimler2507
      @davidzimler2507 2 роки тому

      The DENOMINATOR is smaller, making the overall fraction bigger. 1/2 is greater than 1/5, even though 5 is greater than 2. When you make each number in its own denominator, it flips the inequality.

  • @AsoYasin-n6q
    @AsoYasin-n6q Рік тому

    I'm gonna say it U DID IT BETTER THAN MY TEACHER

  • @SiddharthSrinivasan-ct4jw
    @SiddharthSrinivasan-ct4jw 2 місяці тому

    Carrying me since high school and college

  • @azariaiscool
    @azariaiscool 8 місяців тому

    this is my goat right here brother

  • @siddharthrajagopalan2586
    @siddharthrajagopalan2586 5 років тому

    Thank you for making videos.

  • @georgesadler7830
    @georgesadler7830 2 роки тому +1

    Professor Organic Chemistry Tutor, thank you for another excellent video/lecture on the Direct Comparison Test in Calculus Two. This topic in Calculus Two can be problematic, however students must know the different tests and how to apply them in different cases. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.

  • @jae9932
    @jae9932 Рік тому

    11:50 could you use the integral series test for this?

  • @3lii4Car5
    @3lii4Car5 5 років тому +1

    Thanks God for your existence Doctor 💕

  • @threeoutchange669
    @threeoutchange669 5 років тому

    Here you are saving me again

  • @forrestdangerfield2844
    @forrestdangerfield2844 4 роки тому +1

    Thank you again for your help! So damn easy to understand

  • @muqadasghafoor3611
    @muqadasghafoor3611 3 роки тому

    Amazing video 🙂

  • @otakupenguin8930
    @otakupenguin8930 5 років тому

    This was very helpful

  • @sukhkaur444
    @sukhkaur444 4 роки тому

    Question: "IN THIS VIDEO," if a sub n is inconclusive, do we leave the answer like that? Do we have to solve further to find if a sub n ("an") is divergent t or convergent?

  • @shyamyadla3515
    @shyamyadla3515 6 років тому

    Super explanation sir

  • @helpontheway7856
    @helpontheway7856 6 років тому +3

    You can also cross multiply an and bn to check which is bigger/smaller. Hope it helps someone.

    • @凛-r3h
      @凛-r3h 5 років тому

      why would you do that? isn't it obviously already that 1/(n+1) is smaller than 1/n?

    • @cortiz8726
      @cortiz8726 Рік тому

      @@凛-r3hsometimes its not obvious on harder questions

  • @RAGEEcs
    @RAGEEcs 2 роки тому

    at 12:00 why did ln(n) have to be greater than 1? how did you know to do that?

    • @k-gos
      @k-gos 2 роки тому

      You can refer to the graph of ln x

  • @angelfabian2202
    @angelfabian2202 Рік тому

    so helpful thank you once again !

  • @rodneygolpe3614
    @rodneygolpe3614 5 років тому +1

    In the problem 1/4+ n^1/3 , can't I use 1/n for comparison? 1/n < 1/4+n^1/3. Since 1/n diverges, then 1/4+n^1/3 diverges.
    Correct me if I'm wrong

  • @nathanheath3756
    @nathanheath3756 6 років тому +1

    subscribed! thanks!

  • @aAnNdDyYyGIRL
    @aAnNdDyYyGIRL 2 роки тому

    Thank you thank you thank you 😍

  • @davidotieno1363
    @davidotieno1363 3 роки тому

    Thank you Dr.

  • @beetogarcia9983
    @beetogarcia9983 9 місяців тому

    I understood what was going on after the first example…compared to being almost lost in the sauce in a an hour lecture lol

  • @moazelsawaf2000
    @moazelsawaf2000 5 років тому

    Thanks a lot sir ❤

  • @aaryan505
    @aaryan505 3 роки тому +1

    after watching your video , I hate my maths professor.

  • @elliotjeoffatalifo9656
    @elliotjeoffatalifo9656 4 роки тому

    You have helped me alot

  • @aymmenbatool7254
    @aymmenbatool7254 4 роки тому +1

    If bigger series diverges we cannot conclude the behavior of smaller series, why is it so?

  • @user-ch6xl1zc6k
    @user-ch6xl1zc6k Рік тому

    I don't quite understand how it works in the case of a decreasing series. If bn is larger than an, but both are decreasing then how does bn converging tell us that an also does

  • @razabazal4669
    @razabazal4669 5 років тому

    this is the only reason i am passing calc 2