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
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 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.
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".
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.
@@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
@@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
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
@@longsteinpufferbatch4949 it has a solution (infinitely many actually) in real numbers. if sine is positive and cosine is negative you can get 2 with real input
@@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.
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
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.
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
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!
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 :(
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!
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!
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!
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.🎉
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!
No. 1^infinity is indeterminate. Put it simply, the 0 from 1+0 isn't exactly 0, it's a number very close to 0, and the infinity is the reciprocal of that number.
I am a year 12 student (only like 4 weeks in) and I have never done calculus before however due to unbelievable amount of blackpenred pen content I’ve been watching recently I managed to solve it without ever learning calculus
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 :)
Correct Durgesh, it is a telescoping series where the second term for n cancels with the first term for n+1. However, the to be summed term diverges, so this makes it questionable whether the sum can be said to exist…
Try this one next: ruclips.net/video/Wb30497-7Hg/видео.html
The answer is 4 hrs/day.
well if somebody got a negative number or something thats bigger than 24 its wrong XD
effectivly limiting the window to 0 - 24
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
No it's 4(cos2(x)+sin2(x))
OMG >.
@@SsinaSlx چطوری
Just remember the rule:
Longer the expression, easier it is to solve.
i disagree
I agree
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.
@@amroosha try some of the IMO questions, they are huge and they require huge knowledge too
@@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.
I want my calculus teacher to ask this on test
Right? Haha
Same here
Long aur small both questions are easy to solve
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".
Amazing approach.
Amazing.
Found the investment banker
Jenius
Engineer brain
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.
Thanks so much for your commitment with teaching. People like you make the world a better place.
Thank you 😃
the fact that I’m getting closer and closer to actually solving things like this by myself is scary
lol why
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
@@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
@@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
@@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 😅
Ratio of how scary this one looks to how easy it is solved is just amazing
Exactly opposite to sin(x)^cos(x)=2
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
@@longsteinpufferbatch4949 it does
this has real sol because of this:
(number less than 1)^(negative)>1
@@longsteinpufferbatch4949 it has a solution (infinitely many actually) in real numbers. if sine is positive and cosine is negative you can get 2 with real input
thank you so much for your time and effort you put into these videos! as a calc I student i enjoy them a lot.
Thank you. 😃
Seeing this integral gave me an idea. Is there some kind of recursive integrals where the integration bounds depends on the integral part itself?
As far as I know it's undefined but I'm not totally sure
@@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.
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
That’s a great question. I will think about it. (I haven’t read your reply Bc I wanted to think about it first).
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.
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
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!
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 :(
I could do everything except the series ones, those have always been my Achilles Heel of Calculus
Cmon you can't be saying that with your profile pic
@@cyn8600 it’s been a good 70 years since I’ve studied mathematics, I’m a little rusty
Girlfriend : How do you love me?
BPRP : Integral of....
He is amazing.
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 :)
Oh yea 😆
You make math sound fun and not like a chore, I love ur videos :)
Thank you!
Your videos are always a learning experience.
Love maths but love your videos more ! Thank you 🙏
Thank you : )
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!
Glad to hear 😃 well done!
Thank you for your time ! I wish I had a teacher like you during my studies 😊
Awesome😊😊
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!
i liked yours a lot even tho i didn't know it
You're a blessing to all that yearn to learn thank you bprp
Thank you ! I love your content and personnality. Have a nice day
Thank you.
nicest math you tuber and youtuber at that, always coming in clutch with some cool videos to make my day
Blackpenredpen seems like the coolest professor ever. I would be honored to have a coffee with this guy and talk math
I was able to solve limit and the derivative quickly but can't solve both the series love the question and explanation sir
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!
You are a precious teacher. I'm watching you from Turkey and it helps me a lot. Thank you sir.
or instead of squaring it you could put it to the power the ininite tetration of sqrt(2)
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.🎉
Excelente, professor.
Thanks.
Br
Have a nice christmas Mr Blackpenredpen
You are awesome man!
very creative way of bringing a problem to your subscribers
I dedicate at least 30mins per math video a day when making them
Best thing is that I didn't even really started to study calculus but I understood most of this video
The basic tendeny of human: not matter how easy or hard a question is, if it is long it seems difficult
love your videos bro this video is so wholesome :)
Thanks
Love your videos bprp.
Merry xmas and a happy new year to you too! Thx for all the great videos.
Happy Holiday, have a blessed Christmas.
Finding an answer of a question is at its level, but making such a monstrous "looking" question is at another level.
Happy new year to you too.
Thank you for all your effort! It's always fun to learn something new.
It's true that, if you love what you do, you don't work a day in your life. Your effort is appreciated.
Thank you l!
Best maths teacher I ever had
Never ask him what time is it
😂
You have inspired me a lot ,, from Zambia Africa.
Thank you so much for helping me I am forever grateful for you taking the time to help us.
I like your creativity. Thank you for helping the young scholars!
Happy new year, math guy!
Best way to answer a simple question. Great work, congrats.
Bro you are insane
Dude, I literally understand nothing, but somehow I really enjoy watching these videos
And we're grateful to you!
you do realy excellent work and you re a part of what makes me want to become a math teacher!!
Definition of a problem being way easier than it looks
I simply can't stop watching your videos, really thankful!
Merry Christmas and happy new year professor
Damn! It is so easy ,it took me 2 min to give solution to this question,but i don't even give my 2 hrs to youtube lol.
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!
1:41 I don't understand why the answer is not 1 because (1+0)^infinity = 1 ?
No. 1^infinity is indeterminate. Put it simply, the 0 from 1+0 isn't exactly 0, it's a number very close to 0, and the infinity is the reciprocal of that number.
Why do I watch his videos as a high schooler and not understanding a thing
Ikr
Same
Same
This was actually way easier than I thought!
Thank you Sir.
You're the best
Your videos are my source of joy❤❤
Thank you! Have a happy holidays and happy new year! This man is so cracked he is the GOAT!!!
Just more examples similar to the telescoping series 2:45 ruclips.net/video/IokDRtD1TkM/видео.html
Friend: Bro whats the emergency number...hurry up
blackpenredpen: *hands over an entire integral*
Greetings from Greece.You are very practical 😀
I am a year 12 student (only like 4 weeks in) and I have never done calculus before however due to unbelievable amount of blackpenred pen content I’ve been watching recently I managed to solve it without ever learning calculus
This problem is fierce at the outside, weak at the inside, relatable to most of the teenagers on internet
Hit hard
Need more question like this
You are a great calculus teacher ❤
Missed opportunity to use tetration instead of squaring
Can you answer ( 3125x + 2059)/256= y. ( x and y are integers) find x and y
This guy is amazing.
Now, we can conclude that this person always makes our day 😃🙂
Jus brilliant!!!
Gracias a todos mis maestros de matematicas por enseñarme tan bien como para entender este tipo de videos
Thanks sir ❤❤❤❤
you are amazing!!
While many selected
integrate, limit, series and differentiate
AI : need selected one
A lot of love from India ♥️
This is the final boss of calculus
Keep up the great work 😃
I just have to enjoy 9th grade and enjoy math while it’s still (kinda) easy, looking at this just hurts my brain
This has consumed 100% of my time.
Ya, serious as in drops straight into environmental variables.
Love ur video buddy
Thank you, but as a physicist I am missing the units! :-) 4h/day? 4min/week? 4months/Year?
Very nice video so! :-)
4 hrs / day
@@blackpenredpen No
@@thenewdislikebutton7927 yes
Great video!
I have no idea what you just did but it looked cool
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 :)
Glad to hear thank you.
In ROMÂNIA we learn this things since 17 years old. So this exercise is very easy for us.
Thank u for sharing with us the beauty of math , and merry christmas and happy new year ❤🎊
Thank you too : )
I can't really focus enough to watch all your vids but the ones i do are really good
You are the best bro....
[√(n)-√(n+1)]. Is equal to zero(0), not infinity
Correct Durgesh, it is a telescoping series where the second term for n cancels with the first term for n+1. However, the to be summed term diverges, so this makes it questionable whether the sum can be said to exist…