Increasing, decreasing and not monotonic sequences (KristaKingMath)

[@nolapickering1917]

8 years after you made this and children still worship your knowledge queen, thank you for existing and helping me learn math

[@kristakingmath]

I'm happy to be able to help! :)

[@kristakingmath]

i'm so glad it helped! i use different sources, but i try to go by stewart because he's used more than any other textbook, so he's kind of the definitive source. :)

[@veritasiumaequitasius3530]

Krista, how would you then prove rigorously that a series following the fn of the yellow curve is also decreasing if NOT every n+1 < n? Yes, unfortunately Stewart is used as gatekeeping by stuffy professors who want to condescend and weed out students. It's one of the biggest problems in academia.

[@waltwilliams1770]

James Stewart Calculus 7e does a particularly terrible job of explaining this concept.

[@aaaaaawda]

Walt Williams hahahah welcome to the club my friend welcome

[@corneliuswonderfoot4569]

Lol in the 8th edition it has a terrible explanation too.

[@timothymedina8341]

You're telling me. I'm using the 2e

[@veritasiumaequitasius3530]

8th is no different. Stewart is the "gold standard" for most universities, but it's pretty awful. It's probably popular beacuse it's more cryptic, inaccessible, and makes it easy to condescend to students you're weeding out -- one of the biggest problems in academia.

[@dahazz]

I searched almost every KZbin video, and spent hours on my calculus textbook. Just 10 minutes of thia video cleared every uncertainty. Thanks a lot!

[@kristakingmath]

+Hamza Ali You're welcome, I'm so glad it helped!!

[@kristakingmath]

So glad you like it! :)

[@keanaleong7745]

Hello, @Krista does a sequence have to be both bounded below and above in order to be considered as "bounded"?

[@tonyofearth5100]

Krista King, you the real MVP!

[@kristakingmath]

😀

[@lauraguzman7524]

Wow I just wish I would have found you sooner! You make everything so clear and easy thank you so much

[@kristakingmath]

You're welcome! :) I'm so glad the videos are helping!! :D

[@FerreroRopher]

very helpful, I really appreciate that you went into depth on what monotonic meant

[@kristakingmath]

So glad it was helpful! :)

[@Obsi995]

That was so helpful, appreciate you taking the time! Thanks!

[@kristakingmath]

+Obai Alsamadi You're welcome, I'm happy to help!

[@igobig123]

I was wondering if you had any examples of a sequence like what you are explaining at 3:30. I don't understand why a sequence like this would be considered monotonic! Usually the process of proving a monotonic sequence goes as showing that for ever nth member, a(n) a(n+1)...)

[@salendargoud]

Your teaching is like kristaking ruling the kingdom of calculus. ...Gud work.

[@dilshanisuranga6103]

Few hours of lessons in 11 min. Thank u very much.

[@kristakingmath]

You're welcome, Dilshan, I'm so glad the video helped! :D

[@ritikajain5145]

The yellow line at 3:47 onwards should not be decreasing-monotonic because it has points where for x > y, f(x) > f(y).

[@bassionbean]

Wait... At 3:48, you say that it doesn't necessarily have to decrease at ALL points, but a) you've drawn a continuous function, not a sequence, and b) isn't the proper definition of monotonic decreasing u(n+1) - u(n) < 0? So then a slightly undulating sequence would affect this definition?

[@alcarrion5469]

Your teaching is always helpful. Thank you.

[@abcdef2069]

are you sure the yellow line you drew that is sinusoidally decreasing can be called monotonically decreasing? can we just call it sinusoidally decreasing or just "decreasing", but not as monotonically decreasing? can you double check the terminology? functions like 1/x or log(x) are monotonic functions, they must not have local extremums, it is an important concept in entropy theory

[@rubiyam642]

Pls ask tamil sr

[@leratomoloko496]

11:37 was all it took for me to better understand 2 lectures. Thank you.

[@kristakingmath]

:D

[@21mejia25]

This is not the first time I’ve found the exact problem I need help with on your channel. Thank you.

[@CE113378]

You said that the function is bounded above at 1/5. But this is only true if n>= 1. If you allow n to be 0, then an = 1/3. If you allow n to be negative, then as n approaches -3/2 from the right, the function goes to infinity (and as n approaches -3/2 from the left, an goes to negative infinity).

[@kangmoabel]

Good teacher love it alot from Africa, Ethiopia ❤❤

[@moksha12]

Great instruction, thank you. I'm in Calc II now and I have to miss a few classes next week because of a TDY. Your Vids are helping me to keep up. Thanks Again.

[@kristakingmath]

You're welcome, I'm so glad they're helping!!

[@MM-lb2zk]

Thank you so much for these videos. The way you explain all the different concepts and approach problems is very helpful and fantastic!

[@kristakingmath]

You're very welcome, M! I'm so glad the videos have been helping! :D

[@seanmatisoff1432]

Very clear and easy to understand. Thanks!

[@kristakingmath]

Sean Matisoff You're welcome!

[@hitesh3859]

you are awesome ! you're the real calculus expert ! :)

[@shadesinn6651]

thank you. you explained it so well.

[@kristakingmath]

Thank you, Emmanuel! I'm glad you liked it! :)

[@mr.distasio2945]

Is the sequence at 3:30 monotonic?

[@mohamedrashad2099]

Very helpful Keep doing what your doing Thank you for your time!

[@kristakingmath]

I'm so glad it helped!! :D

[@henrymoore5176]

You are a calculus rock star!!

[@xMartiniquex]

If there are three straight vertical lines on a graph, is that considered to be monotonic?

[@asamonson3475]

Thanks. Good job explaining this. Helped a lot.

[@kristakingmath]

+Asa Monson You're welcome, I'm so glad it helped!

[@harshitshukla2343]

Can you explain the weierstrass function

[@felipe126929666]

Oh my god yes! This was very helpful! Thank you so much!

[@kristakingmath]

Thanks!

[@thomasratliff9278]

Thank you, you are an inspiration. I too desire to teach math one day in the near future.

[@suhailfarooq7831]

Thomas Ratliff ...I also

[@soren81]

Oh, some of my notation got lost there. I'll try again. A function is increasing if and only if the following is true: if x1 is greater than x2, then f(x1) is greater than f(x2).

[@samueloladeji8830]

You are an awesome tutor thank you!

[@kristakingmath]

Thank you so much, Samuel, I'm happy to help! :)

[@AymanFarajat9]

3:30 Big mistake Note that in order for a sequence to be increasing or decreasing it must be increasing/decreasing for every nn. In other words, a sequence that increases for three terms and then decreases for the rest of the terms is NOT a decreasing sequence! Also note that a monotonic sequence must always increase or it must always decrease.

[@AymanFarajat9]

For discussion here my Whatsapp [phone]

[@parthupadhyay7139]

Thanks for this video 😊

[@Callum29D]

sup, inf, max, min. In this case, the infimum is 0 and is not a term of the sequence. The supremum, 1/5 is a term of the sequence. In this case therefore, the maximum of the sequence is equal to its supremum, but the minimum doesn't exist.

[@zanetruesdale8336]

THANK YOU SO MUCH!!!!!!!! I have an exam in five days and this video is amazing! Also, pro-tip for other viewers: turn on the captions and watch the video at x2 speed so you can get through it in half the time. :)

[@kristakingmath]

You're so welcome. Good luck on your exam! :)

[@saralalandeharvey2602]

I determined that {(3-(-1)^n)/(n^2)} was decreasing. However, a(n-1) is not always less then a(n). Why is this? Example n=3

[@M-ABDULLAH-AZIZ]

is a constant sequence monotonic?like {3,3,3,3,3...3,...}

[@akn7097]

I am a bit confused with the definition of monotonic "A sequence is monotonic if it is either non increasing or non decreasing". In this problem, the sequence is decreasing, why do you say it is monotonic?

[@angelohitman]

Well done, grateful for this. I like your voice.

[@slapadashable]

How do you prove that the sequence n power 1/n , is monotonically decreasing ?

[@NaeemIrum]

wah wah wah wah . . bravo . . excellent way of explaing monotonic and bounded sequence. . 👏👏👏

[@kristakingmath]

:D

[@AdnanUrooj]

@KristaKing - Thanks for explaining this :)

[@kristakingmath]

My pleasure, Deminem, I'm so glad it helped! :D

[@GamingAF]

Very helpful thank you

[@millej38]

excellent explanation.

[@kristakingmath]

Thanks! Glad it could help!

[@MRAXELGRINDER]

Awesome video :) Thank you so much

[@kristakingmath]

Thanks, Marko! :D

[@trangdoan415]

Hi, Can you help me with this question: is it possible for a continuous function with the domain R to have f(x)>0, f'(x) 0 for all x ? Thank you.

[@yaminhimani4185]

Why is an+1 less then or equal to an? Shoudn't it be just less than because all the terms could be equal so it woudlnt be decreasing

[@valanraj9414]

Determine which of the following sequence are monotonic 1/(2^n). Please help me for solve this question

[@johng5295]

Thanks in a million. Where have you been all these years.

[@gospeldarko8416]

what have you been watching all this while?

[@FactFrameHub-rz6cz]

monotonicity is a necessary condition for a sequence to be bounded???????

[@Xavaxify]

What about n/ (4n + 1) . Is it strictly increasing or not bounded ? can anyone please explain?

[@xiaostanfirsthumansecond]

you're a lifesaver thank you

[@kristakingmath]

I'm happy to help! :D

[@Donkstar101]

Can n=0? So that a_n is bounded above 1/3 instead?

[@Ayayron_e3]

+Nyugguh yes, but your sequence/series must say that it starts at 0 to some n, and keep in mind n can be infinity.

[@marcwyder5518]

finally a good video. you helped me a lot. Thanks!

[@kristakingmath]

+Marc Wyder Glad you liked it!

[@yyizoy6284]

monotone is increasing or decreasing for all n. So would wave shaped curves in your plot still be considered monotonic? :/

[@drew1436]

+duh duh id assume that it would be considered non monotonic as it is neither increase nor decreases but is bounded from the amplitude

[@chrishandalija8412]

Thank for the wonderful explanation, I will be coming here again whenever i need help😂... Nice Explanation, God bless

[@kristakingmath]

Thank you so much, chrishan! I'm happy I'm able to help!! :D

[@karanveersingh9634]

You are best, thanks for this

[@kristakingmath]

You're welcome, I'm so glad you liked it!

[@kalef1234]

good explanation thanks

[@kristakingmath]

+kalef1234 Thanks!

[@AnDyMaksoud]

Thanks, how did you get so good at calculus :)?

[@XperienceGames]

Very elaborate, thank you!

[@kristakingmath]

You're welcome!

[@binayapaudel3986]

Thank you for your video!!!!!

[@kristakingmath]

You're welcome! Thanks for the comment.

[@nhungbarish4900]

This is great..! thank you..!

[@Gina_Marie_]

Bless this video

[@noose1075]

Please can you help me in solving linear differential equation of first order ( y' = cos x ) please.

[@MrSamson4]

Thank you !

[@kristakingmath]

You're welcome! Glad I could help. :)

[@p.r.p.rodrigo481]

Thank you very much.... ❤️

[@kristakingmath]

You're welcome, happy to help! 😊

[@johnconstantine400]

you are my exam Savior !

[@kristakingmath]

+John Constantine I'm happy to help, I hope you do great on your exam!

[@damianoskgaming83]

Thnk q mam thans alot... Can you teach us about cauchy's sequences i hav a problem in understanding it... Plzzz mam plzz🙏🙏🙏🙏🙏🙏

[@nyikomhangana9812]

THANKS ,U ARE THE BEST

[@kristakingmath]

+nico mhangana Right back at ya!

[@shanpruthi]

super helpful!

[@Fluffy288]

thank you so much this was very helpful!!

[@kristakingmath]

you're welcome, i'm so glad it helped!!

[@vivekvivekt9804]

Love you so much from India

[@usitharanathunga9048]

thank you.....

[@ErkinOrdulu]

You have a beautiful voice.

[@shyamsunder7819]

Thank you, It was helpful !

[@kristakingmath]

Awesome! Glad it could help. :)

[@shyamsunder7819]

Great presentation mam, keep up the good work.

[@soren81]

Your definition of increasing/decreasing, monotonic differs from what is taught in europe. Increasing iff x1 x2 = f(x1) f(x2). Just wanted to mention that. Otherwise great video!

[@humodedam5311]

thank You so much

[@kristakingmath]

You're welcome! Glad I could help.

[@shingool8721]

this is great, thanks a lot.

[@kristakingmath]

you're welcome!

[@PinguExpert]

Thank you a lot!

[@kristakingmath]

You're welcome! Glad it could help. :)

[@ompandey6345]

nicely define very good

[@moazzamalishaikh5598]

Thanks alot🙏🙏🙏🙏🙏🙏

[@kristakingmath]

You're welcome, I'm happy to help! :D

[@3lii4Car5]

Your voice is☹️😻❤️❤️

[@gfff2147]

thanks

[@kristakingmath]

You're welcome!

[@Nirvail0101]

great thanks

[@kristakingmath]

+vansh singh you're welcome!

[@salwaomar1145]

thanks allot ^^ u'r the best

[@kristakingmath]

+salwa omar You're welcome!

[@MinesFavorites]

Well that's pretty awesome. HUGE thanks to you ^_^.

[@rudyruettiger3563]

you're the best!

[@kristakingmath]

awww, thank you so much!

[@robkim55]

Can you find another way of integrating without the usual algorithm......a new way???

[@Dineshkumar-xv4xz]

So good tysm

[@kristakingmath]

You're welcome, Dinesh! :)

[@arianaramseytv]

AMAZING!

[@moazzamalishaikh5598]

Waooooo great delivered

[@kristakingmath]

Thank you, Moazzam, I'm glad you thought so! :)

[@elsharaawy8662]

awesome

[@priyamartis9128]

thank you:)

[@kristakingmath]

You're welcome! Glad I could help!

[@ضحىكريمابراهيمعلي]

Wher is not minotoric

[@iansudheer6ix9ine95]

This is soo unfair,,,...there was your picture on thumbnail!😢