how calculus teacher answers friend’s question

Рет қаралды 497,746

Күн бұрын

How calculus teacher answers friend's question "how much time do you dedicate to KZfaq?". I took about 20 minutes to craft the approximated number of hours per day that I work on KZfaq-related tasks into this beautiful improper integral! This is another all-in-one calculus question that includes a limit, a derivative, a divergent infinite telescoping series, the alternating harmonic series, and an improper integral! I post the picture on Instagram, you can follow me here 👉 / blackpenredpen
Subscribe for more math for fun videos 👉 bit.ly/3o2fMNo
🛍 My merch: bit.ly/bprpmerch, 10% off with the code "WELCOME10"
0:00 the story behind this problem
0:54 start solving this all-in-one calculus problem
5:25 approximately how many hours I dedicate to KZfaq per day
#calculusteacher #blackpenredpen
---------------------------------------------
**Thanks to ALL my lovely patrons for supporting my channel and believing in what I do**
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan Řehák Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R
---------------------------------------------
💪 If you would also like to support this channel and have your name in the video description, then you could become my patron here / blackpenredpen

Пікірлер: 613

@blackpenredpen 8 ай бұрын

Try this one next: kzfaq.info/get/bejne/jchjY5dqnJObeJs.html

@blackpenredpen 2 жыл бұрын

The answer is 4 hrs/day.

@ChadTanker 2 жыл бұрын

well if somebody got a negative number or something thats bigger than 24 its wrong XD effectivly limiting the window to 0 - 24

@SsinaSlx 2 жыл бұрын

Hi professor glad to see you , I'm from Iran , I love math but I'm a student now, I want to use your fabulous and amazing teaching from 0 to up! regretfully I'm not as well as American people in translating during your teaching, could you please guide me about this issue , how can I use the best teaching for learning and understand with all of my cells !!! In more simple language❤❤🔥🔥Thanks

@Roescoe 2 жыл бұрын

No it's 4(cos2(x)+sin2(x))

@graceyu87 2 жыл бұрын

OMG >.

@vaxer.7749 2 жыл бұрын

@@SsinaSlx چطوری

@sujatasharma8560 2 жыл бұрын

Just remember the rule: Longer the expression, easier it is to solve.

@rexthegamergembox 2 жыл бұрын

i disagree

@amroosha 2 жыл бұрын

I agree

@amroosha 2 жыл бұрын

It is because usually short term expressions get expanded then factorized while long term expressions only get factorized only because it isn't logical to be expanded even further.

@rexthegamergembox 2 жыл бұрын

@@amroosha try some of the IMO questions, they are huge and they require huge knowledge too

@Anik_Sine 2 жыл бұрын

@@rexthegamergembox Most of the time when people create large problems, they usually just combine many small questions so that the time taken to solve it is approximately equal to the time taken to solve an average difficult problem. In cases ,like you mentioned, in though exams like IMO they do combine difficult questions.

@rishitpant 2 жыл бұрын

I want my calculus teacher to ask this on test

@readjordan2257 2 жыл бұрын

Right? Haha

@hieu216tdq8 2 жыл бұрын

Same here

@rnikhilkumar9371 2 жыл бұрын

Long aur small both questions are easy to solve

@MalleusImperiorum 2 жыл бұрын

OK, let me solve it for you, guys. His estimate is probably an integer. And since the integer is a square, the possible solutions are 1, 4 or 9. 1 is too little, 9 is too much. The answer should be "4 hours".

@blackpenredpen 2 жыл бұрын

Amazing approach.

@parthpoddar4603 2 жыл бұрын

Amazing.

@omaigad11 2 жыл бұрын

Found the investment banker

@bitoff9125 2 жыл бұрын

Jenius

@thedeaner3117 2 жыл бұрын

Engineer brain

@mayurchaudhari850 2 жыл бұрын

One of the many reasons I love calculus is because you could frame something like that 0:00 in a portrait and it could be worth millions just because it looks beautiful.

@andrewmetasov 2 жыл бұрын

Ratio of how scary this one looks to how easy it is solved is just amazing Exactly opposite to sin(x)^cos(x)=2

@longsteinpufferbatch4949 2 жыл бұрын

How can it be equal to 2? Hmmm shouldn't the maximum value be (1/√2)^(√2/2) Or does this have something to do with complex numbers now. I'm sure it does

@itsnotyourownbusiness827 2 жыл бұрын

@@longsteinpufferbatch4949 it does

@raifegeozay687 2 жыл бұрын

this has real sol because of this: (number less than 1)^(negative)>1

@sylvainstephant2843 2 жыл бұрын

Seeing this integral gave me an idea. Is there some kind of recursive integrals where the integration bounds depends on the integral part itself?

@nickbloons6535 2 жыл бұрын

As far as I know it's undefined but I'm not totally sure

@sylvainstephant2843 2 жыл бұрын

@@nickbloons6535 Why would it be undefined? I actually had several things in mind but for the most simple we can look at an equation like I = Integral from 0 to I of f(x) dx. We are looking actually for some fixed point that is compatible with the integral. For example the integral of 2xdx between 0 and 1 is 1 which satisfies the previous equation.

@nickbloons6535 2 жыл бұрын

Right but then ur just solving for a variable "l" if im reading ur equation right. That's different than having a function of "l". So when I said undefined I was thinking that unbounded would be undefined but you have a good example of a case where it isn't undefined. This kind of reminds me of the Mandelbrot set but with the equation involving integration. I remember putting something similar to this into demos and getting an error msg, but I don't rly understand

@blackpenredpen 2 жыл бұрын

That’s a great question. I will think about it. (I haven’t read your reply Bc I wanted to think about it first).

@chitlitlah 2 жыл бұрын

Some would certainly be solvable. In the example you gave, if f(x) is just x, you would end up with I = 1/2 x^2 from 0 to I, or I = 1/2 I^2. Just off the top of my head, 2 works there. If you're asking if this ever shows up in physics or engineering, I doubt it but I'd love to see an example if I'm wrong.

@ANTONIOMARTINEZ-zz4sp 2 жыл бұрын

Thanks so much for your commitment with teaching. People like you make the world a better place.

@blackpenredpen 2 жыл бұрын

Thank you 😃

@jonhroldan9582 2 жыл бұрын

I really like your channel, specially your latest content about series. I'm taking calculus this semester and the current lessons are about infinite series. Your videos helped me to survive my course. You deserve millions of subscribers!

@drumjunky1608 2 жыл бұрын

I honestly felt proud of myself being able to figure this out and then you solved it in a fraction of the work I needed to solve it. back to feeling dumb again :(

@superrrishabh9982 8 ай бұрын

Keep up your hard work It's very nice to see someone post videos about calculus, Euler's number etc. Not many people take this much time to post such videos Thanks for sharing all the knowledge

@jmtx. 2 жыл бұрын

Thank you for all your effort! It's always fun to learn something new.

@abhaykumarsingh7081 2 жыл бұрын

You're a blessing to all that yearn to learn thank you bprp

@jonnyy1238 2 жыл бұрын

thank you so much for your time and effort you put into these videos! as a calc I student i enjoy them a lot.

@blackpenredpen 2 жыл бұрын

Thank you. 😃

@rrrr3666 9 ай бұрын

Girlfriend : How do you love me? BPRP : Integral of....

@cauedemelosilva4381 2 жыл бұрын

Best way to answer a simple question. Great work, congrats.

@fisicaenpastillas8768 2 жыл бұрын

I simply can't stop watching your videos, really thankful!

@balathevar1828 2 жыл бұрын

I like your creativity. Thank you for helping the young scholars!

@moinmalik1320 Жыл бұрын

Your videos are always a learning experience.

@Sanwichgamingtr 2 жыл бұрын

You are a precious teacher. I'm watching you from Turkey and it helps me a lot. Thank you sir.

@alberteinstein3612 2 жыл бұрын

I could do everything except the series ones, those have always been my Achilles Heel of Calculus

@cyn8600 2 жыл бұрын

Cmon you can't be saying that with your profile pic

@alberteinstein3612 2 жыл бұрын

@@cyn8600 it’s been a good 70 years since I’ve studied mathematics, I’m a little rusty

@RB79RB 2 жыл бұрын

Merry xmas and a happy new year to you too! Thx for all the great videos.

@oliguilo 2 жыл бұрын

Thank you for your time ! I wish I had a teacher like you during my studies 😊

@DhirajjMahatoo 6 ай бұрын

Awesome😊😊

@gasorpasorpasorpasorpobrow7419 2 жыл бұрын

you do realy excellent work and you re a part of what makes me want to become a math teacher!!

@babai08_ 2 жыл бұрын

Love your videos bprp.

@global169 2 жыл бұрын

Thank you so much for helping me I am forever grateful for you taking the time to help us.

@user-yz3he2jm4o 8 ай бұрын

He is amazing.

@ZamanAristoOrCleon 2 жыл бұрын

Thank you! Have a happy holidays and happy new year! This man is so cracked he is the GOAT!!!

@alexrozenbom3430 2 жыл бұрын

Happy new year to you too.

@petereziagor4604 2 жыл бұрын

Thank you Sir. You're the best

@IMAN_IIT_PATNA 2 жыл бұрын

Now, we can conclude that this person always makes our day 😃🙂

@lite7769 2 жыл бұрын

You make math sound fun and not like a chore, I love ur videos :)

@blackpenredpen 2 жыл бұрын

Thank you!

@sunny_25 8 ай бұрын

very creative way of bringing a problem to your subscribers

@mcgrewgs 2 жыл бұрын

1:44 "If you want to make any calculus equation look harder, replace all the 1s with sin^2(x)+cos^2(x)" 🤣🤣 I'd also suggest replacing all the π with sqrt( 6*sum_{n=1}^{\infty}(n^{-2}) ) for extra fun 😊 Merry Christmas to you, too!

@Z7youtube Жыл бұрын

i liked yours a lot even tho i didn't know it

@pierre7770 2 жыл бұрын

Love maths but love your videos more ! Thank you 🙏

@blackpenredpen 2 жыл бұрын

Thank you : )

@rafaelbelda6140 2 жыл бұрын

you are amazing!!

@Amb3rjack 8 ай бұрын

Jus brilliant!!!

@spider-uh5ws 2 жыл бұрын

Have a nice christmas Mr Blackpenredpen

@Etienne-JEUNEHOMME 2 жыл бұрын

Thank you ! I love your content and personnality. Have a nice day

@blackpenredpen 2 жыл бұрын

Thank you.

@rohitranjan4416 2 жыл бұрын

You are awesome man!

@asdjhasdgayhuioawe 2 жыл бұрын

Keep up the great work 😃

@noodlesandsteak 2 жыл бұрын

the fact that I’m getting closer and closer to actually solving things like this by myself is scary

@blackpenredpen 2 жыл бұрын

lol why

@cxllmegeo3557 2 жыл бұрын

I’m in 10th and decided to just look at this and I’d I’m already discouraged. But I hope I can solve stuff like this in the future

@marshian__mallow2624 2 жыл бұрын

@@cxllmegeo3557 don’t be discouraged by hard looking maths. Hard looking maths isn’t what you should worry about. It’s the “easy” questions that get you

@levi2732 2 жыл бұрын

@@cxllmegeo3557 im economist but i do maths for fun and i can solve this easly , it's nothing compare to inferential statistics, but one day you will understand thos things and the logique of MATH just be patient

@cxllmegeo3557 2 жыл бұрын

@@levi2732 I appreciate the encouragement. Can u explain what inferential statistics is cuz I just looked it up and I still don’t get it 😅

@Nutshell_Mathematica Жыл бұрын

Need more question like this

@ardakara2003 Жыл бұрын

Your videos are my source of joy❤❤

@saltyconsolegamer9383 2 жыл бұрын

nicest math you tuber and youtuber at that, always coming in clutch with some cool videos to make my day

@gilgameshur-nammu366 2 жыл бұрын

Blackpenredpen seems like the coolest professor ever. I would be honored to have a coffee with this guy and talk math

@Anik_Sine 2 жыл бұрын

The basic tendeny of human: not matter how easy or hard a question is, if it is long it seems difficult

@gilgameshur-nammu366 2 жыл бұрын

I wanted to say that I really appreciate you for being so welcoming and friendly and showing us that math can be fun -- and not so scary after all! Some professors are condescending, but you can tell that blackpenredpen is a wonderful professor that loves his jobs, and loves teaching! Cheers!

@Ou_dembele 2 жыл бұрын

Merry Christmas and happy new year professor

@greghansen38 2 жыл бұрын

And we're grateful to you!

@goku-mx5ew 2 жыл бұрын

I was able to solve limit and the derivative quickly but can't solve both the series love the question and explanation sir

@ilariae346 2 жыл бұрын

I love this video, hnoestly the highlight of my day!!:)

@josephpalad7815 2 жыл бұрын

Happy Holiday, have a blessed Christmas.

@nataodutton4344 2 жыл бұрын

love your videos bro this video is so wholesome :)

@blackpenredpen 2 жыл бұрын

Thanks

@carlosomarmartinezcarmona1485 2 жыл бұрын

Gracias a todos mis maestros de matematicas por enseñarme tan bien como para entender este tipo de videos

@pythonholic 2 жыл бұрын

Thank you so much 💓

@user-bf7iz2tz1i 2 жыл бұрын

Great video!

@leprofeet9989 2 жыл бұрын

Happy new year, math guy!

@tonyhaddad1394 2 жыл бұрын

Thank u for sharing with us the beauty of math , and merry christmas and happy new year ❤🎊

@blackpenredpen 2 жыл бұрын

Thank you too : )

@Mathematics-wp6ti 8 ай бұрын

You are a great calculus teacher ❤

@PerseoRapax 2 жыл бұрын

Sois el mejor profesor de KZfaq, sigue así crack.

@blackpenredpen 2 жыл бұрын

Just more examples similar to the telescoping series 2:45 kzfaq.info/get/bejne/f9Wbd7WlqZe4m4E.html

@achalanand2213 2 жыл бұрын

This guy is amazing.

@yunghollow1529 2 жыл бұрын

A brilliant yung man that has a Kung Fu master beard with a pokemon ball in his hand doing calculus YT videos.. That is something i've never expected to see even in a million years. BTW i found your channel recently & really love your content.. Keep it up sir

@UROOZFATIMA190 6 ай бұрын

Wow great content and your subscription is here i am a mathematics ❤and physics lover and your videos are so amusingly AWESOME so marvelous work keep it up.🎉

@dylanmcgowan8999 2 жыл бұрын

or instead of squaring it you could put it to the power the ininite tetration of sqrt(2)

@MohitKumar-eu4pz 2 жыл бұрын

Love ur video buddy

@SUPERIDOLLOVER 2 жыл бұрын

Best maths teacher I ever had

@sreedharbodigalla2569 2 жыл бұрын

Tq u so much sir... Most usefully 🌹

@mextitan 2 жыл бұрын

You sir, are a saint, among other youtubers helped understand calc 2,calc 3, and calc 4. I had not taken any college courses in 10 years, and with your help I was able to pass with two A's and a B. So thank you for your time!

@blackpenredpen 2 жыл бұрын

Glad to hear 😃 well done!

@luizkemo 2 жыл бұрын

thanks a lot for all your content, you really taught calculus to me and now i feel so comfortable using it on everywhere i can (lol) im so greatful, thank you bprp :)

@blackpenredpen 2 жыл бұрын

Glad to hear thank you.

@pablohurtado3505 2 жыл бұрын

You are the best bro....

@michaelahklein 8 ай бұрын

i love this :)

@mwiibakuyokwa1354 2 жыл бұрын

You have inspired me a lot ,, from Zambia Africa.

@khemlyhourt4178 2 жыл бұрын

I always support you.

@lilbanana6159 8 ай бұрын

Friend: Bro whats the emergency number...hurry up blackpenredpen: *hands over an entire integral*

@the_mashinist2023 2 жыл бұрын

Greetings from Greece.You are very practical 😀

@mikefochtman7164 2 жыл бұрын

I admit that I say the telescoping and the alternating harmonic, but the rest was a surprise. Happy Holiday and thank you for your work, I enjoy your videos.

@patrickboner 2 жыл бұрын

I can't really focus enough to watch all your vids but the ones i do are really good

@vloyolaa 2 жыл бұрын

Thanks for your work. And greetings from Perú

@ioangauss 2 жыл бұрын

4:02 just explain that if you change n=u+1 from the normal serie equals to lin(1+x) you fall on the one you have onyour whiteboard :)

@blackpenredpen 2 жыл бұрын

Oh yea 😆

@SandeepKumar-dw3sj 2 жыл бұрын

You guy is awesome 👏👏👏 I try it many times & when I saw it full ved. & My expression is omg👍🇮🇳👍

@xdkiller1385 8 ай бұрын

I'm in the 9th grade and I'm getting very close to solving these on my own! It'll be very exciting for me to do a problem like such on my own, and I hope that's soon!