Direct Comparison Test - Calculus 2

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/gnPbioRmia-rj68 Final Exams and Video Playlists: www.video-tutor.net/

[@Idurangalk]

Isn't 1/n convergent

[@audiomac]

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

[@MukyalaDoreen]

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

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not anymore lmao

[@aunpaidintern7035]

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.

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aunpaidintern ! Good luck man

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[@rmdir]

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]

what a nice way to explain it thanks man

[@ziaddd6919]

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

[@MeinCouch123]

Very very nice way to put it 👍

[@Silenwrld]

That's deep man😊

[@Silenwrld]

10:34

[@claireeckhardt4472]

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!!!

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[@terrancepage9163]

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

[@pfeliciano4062]

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

[@RamytRamyt]

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!!!!

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

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

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

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@@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.

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

[@LongRangeBacon]

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

[@maktub_txt]

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]

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

[@maktub_txt]

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

[@Giblet12]

@@maktub_txt Thanks my man

[@celineguler]

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]

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

[@TMAJ0R]

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

[@annpham6455]

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

[@nvn7291]

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.

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

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[@clutchmadness]

@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]

because the numerator becomes insignificant compared to the denominatoe?

[@rambhayadav9854]

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

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What a wonderful lesson. Keep it up.

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The savior of my calc grade

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[@zekebranham9997]

Amazing explaination

[@adabujiki]

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.

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These videos are so helpful!! Thank you!

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Thanks is most useful your video than others.

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you're so good at teaching

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Most concept full channel

[@RealPixelFusion]

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?

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

[@georgesadler7830]

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 KZbin TV with the Organic Chemistry Tutor.

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

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[@hannanbaig7888]

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

[@pfeliciano4062]

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

[@pfeliciano4062]

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

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The examples are very simple!!!

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Thank you Dr.

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[@humbatgasimov6452]

Wonderful video.

[@reidgarrison9629]

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

[@muqadasghafoor3611]

Amazing video 🙂

[@aAnNdDyYyGIRL]

Thank you thank you thank you 😍

[@zarkmuckerberg8341]

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

[@squidcurry9955]

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

[@mahamadmarshall9031]

Bro u think of p series

[@3lii4Car5]

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[@papuan-black]

Thank you ❤

[@jae9932]

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

[@SiddharthSrinivasan-ct4jw]

Carrying me since high school and college

[@otakupenguin8930]

This was very helpful

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[@nathanheath3756]

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[@audiomac]

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]

thanks

[@audiomac]

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

[@minkihairoil]

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]

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.

[@hafsamohamad1597]

Thank you so much

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after watching your video , I hate my maths professor.

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I love this thank you

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

[@user-ch6xl1zc6k]

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

[@sukhkaur444]

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?

[@maxdegreat566]

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

[@amankikani4354]

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

[@johnperez3454]

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.