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.
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.
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!
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!!!
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
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.
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!
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
@@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.
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.
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?
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?
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 RUclips TV with the Organic Chemistry Tutor.
Insignificant meaning that the value barely changes the denominator. For example, if you have a value of infinity such as 100,000,000. The +5 wont change the value much as it is still infinity.
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
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Isn't 1/n convergent
@@Idurangaa 1/n is convergent, but its series is not. Look up p-series to look up more on the topic.
❤
My man is carrying the entirety of the next generation's higher education on his shoulders
The most underrated channel
ikr
@Txawjntse Vang wuzzy
@Txawjntse Vang lol I was not expecting that reply so I actually laughed.
Lmao he has over 2 million subscribers. Most don't take calculus and many avoid it at all costs.
not anymore lmao
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.
what a nice way to explain it thanks man
thanks for this, my professor was so confusing when he explained it
Very very nice way to put it 👍
That's deep man😊
10:34
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.
aunpaidintern ! Good luck man
How tf did you survive that
All the best bro
wtf when do you sleep
bro best of luck..
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!
you and patrickjmt are the people i pray to thank you everynight
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.
Sameee ☺️☺️☺️
@@bicboi46 its just something dope doing math
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!!!
Hey, good luck and don’t give up! RIP to your awesome calc teacher
You are just awesome. Consistently through the past year, whenever I've struggled to understand a concept or technique, your videos make it click.
that graph visual really helped me understand things so much clearer! thank you!!!
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!!!!
you're a life saver, thank you so much 😭❤
excellent video. I feel twice as ready for my exam tomorrow.
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
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
thanks my teacher you're a good teacheer
Remember if An=< Bn it will converge unless An goes to negative infinity
I get so sad whenever he says "This is the last example for this video''
I can always count on this channel for the 2am next day exam cram
honestly my best teacher on youtube
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.
u r a math god, thank u for humbly serenading us w ur godtier wisdom
Amazing explaination
I made it to calc 2 and I'm so happy.
Most concept full channel
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!
The savior of my calc grade
I don't even have to go to class, I just watch your videos before my quizzes. Good stuff man
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
Haha same boat here. Exam is in 21 hours for me
@@Giblet12 *cries in calculus*
Best of luck ✨
@@maktub_txt Thanks my man
you're so good at teaching
You saved my life mann great presentation
Thanks a lot sir 👍. I got cleared the concept of direct comparison test . I wasn't knowing it so clearly .
Thanks is most useful your video than others.
8:56 why inconclusive? we didn't check a smaller series but by just a bigger series is divergent we say it's inconclusive?
what else is there to check? You use limit comparison test if you get inconclusive
I always watch this guys videos before the lectures by my professors... always.
As an engineering student at Purdue, may you be blessed in all facets of life. We love you.
How is Purdue for engineering?
I was thinking of transferring
@@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.
@@hayley863 Hey thanks for the response. I just might see you there if my grades hold up :)
@@hayley863You graduate?
@@vipari I did, but from a different school. I actually ended up transferring to a school in my home state :)
Thanks a lot for saving my calc grades
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.
The examples are very simple!!!
What a wonderful lesson. Keep it up.
It really helps , even though I don’t know english
it's another moment of when foreigners say they don't know english but speak way better than the natives.... respect
LITERALLY SAVING MY LIFE
Thank you Dr.
god bless you man thank you so much from turkey 🇹🇷🇹🇷
@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 :)
because the numerator becomes insignificant compared to the denominatoe?
I love you ❤ you are awesome i had wasted 4hrs trying to understand this you made me understand this in 15 mins.🥺🥺🥺 love you
Thanks man.You are a life saver
You are the best, that all what I can say, thank you my legend ❤️
he's gonna save my semester yehe ; -- ;
best content ever very usefull thank you for everything
These videos are so helpful!! Thank you!
Here you are saving me again
I LOVE YOU SO MUCH thank you for all the videos!!!
Thanks a lot. I'm liking the new colors. It looks great
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most loved youtuber fo sho lmao
Super explanation sir
You have helped me alot
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.
tatia a why ?
danny camello I need to put a face to it
He probably looks like an angel
or the face of god
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I bet you never thought how important your channel would be
This was very helpful
Thank you very much, I hope you keep going up to diff
Thank you this was really good and helpful!!!!
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?
Omg thank you very much bro. You helped me
Thank you so much
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?
More more more more...🙏 thank you😍🥺😘😘
Thanks God for your existence Doctor 💕
Thanks Jesus Christ 🙏
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
this is my goat right here brother
Thank you for making videos.
In the second last example. the series 1/n is convergent. correct it.
kind regards!
nope! diverges since its harmonic after simplifying and if you do the p-test, it diverge since its equal and less than 1.
@@erikaguevara3002 My bad! I got it.
Thanks
Thanks a lot sir ❤
this is the only reason i am passing calc 2
Superbb keep making 👍👍👍👍👍👍👍
in class i was lost, on hawks i was confused on yt it all makes sense lol thanks
Thank you thank you thank you 😍
Thank you
Thanks dude
Isn't (1/3)^xthe P-series? I thought Geometric series is more like AnX^n... I'm confused...
Amazing video 🙂
so helpful thank you once again !
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 RUclips TV with the Organic Chemistry Tutor.
I love this thank you
You are woderful
If bigger series diverges we cannot conclude the behavior of smaller series, why is it so?
so helpful
thanks this lecture solve my problem about comparison test
what do you mean by "insignificant" in this case?
Insignificant meaning that the value barely changes the denominator. For example, if you have a value of infinity such as 100,000,000. The +5 wont change the value much as it is still infinity.
You can also cross multiply an and bn to check which is bigger/smaller. Hope it helps someone.
why would you do that? isn't it obviously already that 1/(n+1) is smaller than 1/n?
@@凛-r3hsometimes its not obvious on harder questions
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
I would be proud to shake this mans hand
at 11:53 why didnt you consider ln(n) / n (the bigger series) instead of 1 / n (the smaller series)?
Hannan Baig yeah I was confused, because if you were to plug in any number the bigger one would be 1/n
Oh I figured it’s because we had a restriction of n is greater than or equal to 3
Thank you again for your help! So damn easy to understand
Thank you ❤
thanks
thankyou so much...
10:55 why cant we use L'hospital rule when n goes to infinity wouldnt the bid series go to zero ?
shokran yasta