Here are the Time Stamps! (Q1) 0:04 circular metal plate (Q2) 5:57 water in a circular tank (Q3) 16:02 the ladder falling down (Q4) 24:21 two cars approaching to the same intersection (Q5) 32:38 two ships, one ship travels north the other travels south (Q6) 42:13 two sides of a triangles are changing (Q7.) 50:08 balloon rising up and angle of inclination If you like this video, be sure to subscribe for more math related content. Also help me to share this video with your calc classmates and teachers, thank you!
@clashroyalepro9082
5 жыл бұрын
Can you explain this sir please why the integration of sin6x is -cos6x/6 ? With proof .....
@tomjohn3644
5 жыл бұрын
When will the shirt in your profile pic be available to buy as merchandise?
@aashsyed1277
3 жыл бұрын
thank you so much! =D
@alinamoreno9235
3 жыл бұрын
THANK YOU KING! you're saving both my grades and my sanity this semester
@blackpenredpen
3 жыл бұрын
Glad to hear 😃
@tiredpoe5540
2 жыл бұрын
Same I started to fall behind. Hopefully this would make me be ahead.
@JB1RD367
5 жыл бұрын
Fantastic! I'm actually teaching this topic in two days and I'm going to use your method of explanation to help. The two pictures is a great idea.
@blackpenredpen
5 жыл бұрын
Johnathan Tafoya nice!! Let me know how it goes!
@zynex9250
10 ай бұрын
This is a REALLY well made video
@alissa7760
3 жыл бұрын
You are a life saver 😭😭😭😭 and thanks for explaining every single step so well. It’s the video I’ve been looking for for hours and hours today..... finally found the video I was looking for 😭❤️ Love it!!! Please keep up the good work!
@rkumaresh
8 ай бұрын
With 7 different problems one can do any problem on related rates. All are great explanations . The ball problem could be done alternatively by differentiating the equation tan(theta)=h/500 w.r.to t where we should determine sec^2(theta) using the given information and then substituting into the derivative equation i.e sec^2(theta) times d(theta)/dt = (1/500) times dh/dt.
@THotSouce
4 ай бұрын
You're ridiculously helpful man, thanks for this amazing content and your effort
@belutcodm2850
Ай бұрын
I find your videos to be really helpful so I'm here to leave my comment
@JamalAhmadMalik
5 жыл бұрын
Thanks, at any rate!
@blackpenredpen
5 жыл бұрын
lol
@xcalibur6482
5 жыл бұрын
My math exam was good... but im not sure about a six mark problem... doesnt matter... exam or not... i will solve it... i will learn it... maths is about learning from mistakes 😊😊😊
@rofl.connoisseur
4 ай бұрын
thats the spirit
@LS-Moto
5 жыл бұрын
I can't catch up with all these videos 😂 .... good luck to everyone writing calculus 💪
@comprehendnature2404
2 жыл бұрын
I think I understand it now. First, you find a geometric formula that apply to the problem, then convert it to a derivates problem, derivate it and make sure that you isolate the one you want to find. Its easy now that I understand it. I will work on more problems to make sure I get it right.
@drpeyam
5 жыл бұрын
Neat! It’s almost as if this video and the 100 integrals video are... related 😉
@blackpenredpen
5 жыл бұрын
Dr Peyam Hahahhaha
@rob876
5 жыл бұрын
I prefer to derive the equations first and only plug the numbers in last of all. There's less chance of an arithmetical mistake that way. e.g. for the ships problem, I would get dC/dt = f(t) and then compute f(4).
@satyam-jha
5 жыл бұрын
I first tried to solve the following problems by my own then after looking at the solutions and YAY I succeeded in 6/7. Amazing content keep it up...😀😀😀
@blackpenredpen
5 жыл бұрын
Satyam Jha yay thank you!!
@satyam-jha
5 жыл бұрын
@@blackpenredpen just keep it up.. Proud member of calculus finisher.:p
@johnabraham8520
4 жыл бұрын
Satyam Jha which one you got wrong ?
@quixiee_
7 ай бұрын
Finally, things are making sense.. thank you 😊😊
@con_el_maestro3544
Жыл бұрын
Sir, I got every single one of those questions wrong except for question 7, I think I get it now... There are no words to describe how grateful I am except to say THANK YOU ❤🔥
@unknownme5930
5 жыл бұрын
Please do more worksheet videos like this !! Its really helpful,thank you so much :))
@user-sy2vd3kn2x
5 жыл бұрын
Greek school books use this problems at the rate of change chapter.
@epicfacelover
2 жыл бұрын
Thank you for the help, literally all of these were on my homework!
@owenscinta1032
2 жыл бұрын
so concise did better than a uni professor I pay 70k a year to be in his class.
@GeletomWAbebe
3 жыл бұрын
From the 7 examples one or two of them will appear on our national exam (g-12) and i want to say thank u for your dedication
@MusicalInquisit
2 жыл бұрын
For question six, the units for the derivative of area with respect to time is not simply meters-squared per second. Because the derivative of area includes rad/s as a multiple, the unit for the change in area is in actuality (meters per second)-squared times radians
@NasirKhan-lq5jl
5 жыл бұрын
I love the content!!! Can you please do some videos on Complex Analysis by any chance...
@kauze8063
5 жыл бұрын
ooooo. Related rates😉 my favorite
@HeYoNiA
3 жыл бұрын
Saved my skin! I didn't know what to do until I found this video, thanks man!
@alejrandom6592
3 жыл бұрын
I can't believe I actually solved the first problem, I haven´t seen these before lol. I used integration to figure out that r(t)=0.02t plugged it into A=pi*(r(t))^2, so I got A=pi*0.0004t^2, then I set 60=0.02t to solve for t=3000 differentiating A I got dA/dt=pi*0.0008t, plugged in t=3000 into this derivative and got 2.4*pi :D
@michaeldengg
3 жыл бұрын
oh you shouldn't really use what t=, its much easier to solve it using just normal differentiation
@HorizonSpeed26
5 жыл бұрын
on q5 I used the limit definition of the derivative lol. I think I might be a bit too ahead of myself with this stuff.
@alexgutierrez4547
10 ай бұрын
Thank you so much!! Helped so much
@gloriaa5857
2 жыл бұрын
This video what so easy to follow, Thankyou!!
@blackpenredpen
2 жыл бұрын
Glad it was helpful!
@minlehya1163
2 жыл бұрын
THANK YOU, YOU ARE THE BEST
@fiona685
Жыл бұрын
Thank you so much for the amazing explanation! Simple and super clear!
@SarahStarmer
9 ай бұрын
Thanks this is very helpful.
@scrumptious1227
4 күн бұрын
I have a question on 30:28 about that sketch
@diagasokhna5777
4 жыл бұрын
car A and B( can you please check it again)!!! I f the car is heading north which means it's increasing, right? my final answer is 18mph.
@blackpenredpen
4 жыл бұрын
No, because they are heading toward the same intersection.
@multipleorganfailure3449
3 жыл бұрын
Helpful for sure. Great video. Thank you.
@slyanover
2 жыл бұрын
Thanks, great explanation, especially the two diagrams.
@Anna-qp1fi
3 жыл бұрын
Thank you so much!
@newtonnewtonnewton1587
5 жыл бұрын
Nice i am amath teacher its an easy quistion in our school here in jordan there is many quistion more difficult than this quistion
@portreemathstutor
9 ай бұрын
Thank you.
@williamwelmans8648
Жыл бұрын
Thank you!
@einavrubin6353
2 жыл бұрын
Thank you so much!!!!!!!!!
@michaeldengg
3 жыл бұрын
I got every question right but Q2, Q5 and Q7... Thanks for the help though I sorta struggling on this subject...
@catherinehill8198
Жыл бұрын
Thank you
@andrewbooths7099
2 жыл бұрын
Very helpful. Thank you. Keep it up.
@gustavosedano294
5 жыл бұрын
Very usefull before an exam
@gaurangagarwal3243
5 жыл бұрын
21:02 oh I knew it atleast. 😁Just kidding. Btw awesome viddeo
My geometric intuition stinks. For the two ships problem, I more likely than not wouldn't have figured out the ships' bearings relative to each other formed an increasingly large right triangle if I had not seen you work this problem a couple of dozen times. Therefore I decided to work it using vector algebra. Each ship has a position vector that explicitly depends on time. As such the difference in their positions is also a time dependent vector. The position of B relative to A is given by: R = 100 *i* + 60t *j* . The magnitude of R, the distance between the two ships, is given by |R| = sqrt[ 100^2 + (60t)^2 ]. Differentiating with respect to time gives the expression d|R|/dt = 3600t/sqrt[100^2 + (60t)^2 ]. Substituting t = 4 into this expression gives d|R|/dt = 14400/260 = 55.385 kilometers per hour. ◼
@lalitverma5818
5 жыл бұрын
Wow u r great teacher
@jammonmd
2 жыл бұрын
Regarding Q2: Am I the only one who thought an inverted cone would have the large part on bottom? That would change the answer. Love your videos!
@jammonmd
2 жыл бұрын
In that case, I got dh/dt = 24/(13 pi)
@babs8233
2 жыл бұрын
I though the same thing! drew it like that too....
@natejones8508
2 жыл бұрын
ice cream cone is inverted, traffic road cone is regular LOL
Why do you use the chain rule in the first problem? It’s not a composite function to my understanding
@soumikpal8910
5 жыл бұрын
Sir can you please explain when 1^m=1^n (m is not equal to n) then it seems like m=n and we can prove every real number is equal to another real number . Btw love your vids 😇
@NasirKhan-lq5jl
5 жыл бұрын
Essentially what you did is took logarithm both the side to base 1. But it's actually not like that as logarithm base b is as 0 or 1 not =b. Or else you there would be troublesome situations like you have encountered.
@typo691
5 жыл бұрын
In order to get from 1^m=1^n to m=n, you would need to take log base 1 but because of the very problem you pointed out, log to base 1 is undefined
@hamiltonianpathondodecahed5236
5 жыл бұрын
@@typo691 u can also take log any base but it will end up log some base of 1 which is zero.
@danielmacsai776
5 жыл бұрын
One to any power is one
@hamiltonianpathondodecahed5236
5 жыл бұрын
@@danielmacsai776 what about 1^inf
@Skankhunt-mv4vd
5 жыл бұрын
This might be a stupid request, but heck it! I recently noticed that there is a very high chance that you get a pair of any two numbers (not taking the suit into account) in a deck of cards i.e. 2 and 2, queen and queen, 10 and 10 and so on.. I was trying to calculate an actual probability for this phenomenon and really struggled. I would appreciate it if you did a video over this problem, or if it seems really simple for your audience, a general probability video would be greatly appreciated. Thanks!
@blackpenredpen
5 жыл бұрын
Skankhunt 42 how many cards are we choosing?
@Skankhunt-mv4vd
5 жыл бұрын
blackpenredpen not choosing any number of cards. When u shuffle the deck, it is almost guaranteed that you will get a pair of cards that are the same when you go through the whole deck. all the 52 different cards.
@asiaakperov6479
3 жыл бұрын
For question 6: how did you simplify the last bit --> 20cos(pi/3)(.06) become .6
@ajanar
2 жыл бұрын
1.199 in my calculator
@samiadam3632
2 жыл бұрын
20×.5×.6=6 COS 60=.5
@gordonchan4801
5 жыл бұрын
There is a slight error in the PDF document. The unit for question 7 should be "rad/s" instead of "ft/s".
@ahmad_hun
Жыл бұрын
Sir are you using calculus and analytical geometry by Thomas ?? And I can't find play list can somebody help me ?
@otioti264
5 жыл бұрын
Where can I find those pen?
@thrivikramsasapu2253
2 жыл бұрын
i know its a bit late but generally when we think of a ladder and the bottom part is moving with a certain rate then the top part should also move at the same rate right ,if not can you explain what makes it move at different rate when compared to the bottom part...
@science-y9209
3 жыл бұрын
How did you randomly assume that it would be 12 oclock and not 11 or 1 oclock ... how can you be so sure.. please tell me.. (Q5)
@jadensmith2191
Жыл бұрын
Why can't I use radius in question two?
@Sidou_
5 жыл бұрын
Please Can you show US the integral of sqrt(x)*cos(x)
@alissa7760
3 жыл бұрын
Can you please do the shadow related questions to please
@aldricbenalan4755
4 жыл бұрын
CHEN LU!!!!!!
@jasonloftis9563
Жыл бұрын
Respectfully, I believe the answer to the ships problem is incorrect. I followed every step several times, down to the "use your calculator" part, and I get 73.8. Incidentally, I found another video involving the exact same question with the only difference being the ships' speeds, A being 35 and B being 25, and that video's solution is the one you presented. Did you alter the ships' speeds but forget to adjust the solution?
@chikenwingsteve
Жыл бұрын
Nope. The correct answer is 55.4
@rik9833
2 жыл бұрын
when you took the derative of the whole equation with respect to t at 3:35, why couldn't we take the derative of pie, which would be 0 because derivative of constant is always 0
@waldo719
2 жыл бұрын
Constants only turn into 0 when it doesn’t have a variable with it. You can also just imagine the constant beside a variable with zero exponent. [for example: (d/dx)3 is just the same as (d/dx)3x^0 since anything with zero exponent is just 1. Taking its derivative will just bring the zero down which is why we cancel constants when differentiating.]
@user-pj9tk4op4w
2 жыл бұрын
dA/dt is actually speed , velocity when you apply Pythagorean theorem you referred to distances and not velocity!!!!
@preciousjumuad2958
2 жыл бұрын
I rushed answering coz I wanted to hear Doraemon theme song intro every cut XD
@forthesakeofscience961
5 жыл бұрын
Hey hi answer this Can u pls do a differentiation under integral sign video plzz
@JensenPlaysMC
5 жыл бұрын
kzitem.info/news/bejne/k4CK359rfHSnmH4 and kzitem.info/news/bejne/1Gewzo16bapnoI4
@saharhaimyaccov4977
5 жыл бұрын
Can u show graph with I number ..?
@namenlos4198
5 жыл бұрын
Is it assumed in Q2 that the inverted cone is regular so that the apex lays in the middle of the base circle?
@namenlos4198
5 жыл бұрын
Or can we use Cavalieri's Principle to simplify the question?
@joshuaargote3231
5 жыл бұрын
Where do you even get these questions?
@neilgerace355
5 жыл бұрын
4:07 What is this "chain rule"? ;)
@cyan1153
2 жыл бұрын
For question 2, is height measured in m^3/min or m/min? This question has been bugging me for a few days now.
@raexn
Жыл бұрын
Height is one dimension. Therefore, m/min.
@n-clue2871
Жыл бұрын
pov: youre in elementary but you get a question right
@assbeater5642
4 жыл бұрын
I LOVE U
@ricktomev155
2 жыл бұрын
Black pen blue pen
@ssdd9911
5 жыл бұрын
i thought do be4 already?
@iCosmicRex
3 жыл бұрын
shouldn't the answer at the end be 14/50?? or 7/25 if you simplify it. you have 140/500 so i think there is a slight error. amazing helpful nonetheless!
@chikenwingsteve
Жыл бұрын
No. You are wrong. 1+1 = 2 2 x 500 = 1000 140/1000 = 7/50, not 7/25. Your welcome
@clunkymonkey1403
3 жыл бұрын
people in the us are taking this in college while I am taking this in 10th grade.......FUCK
@HoSza1
5 жыл бұрын
The ladder example is suspicious because the ladder will detach the wall at some point.
@marcushendriksen8415
5 жыл бұрын
Wow, you're really making me think about this. Common sense agrees with you that the ladder would detach from the wall at some point, but I'm not so sure. For the ladder to not touch the wall, the overall distance between x and y would have to increase, and I'm pretty sure that calls for an acceleration. The problem mentions a constant d/dt for x and y though, so no acceleration to be had there. I think in the real world, you're actually right, because such a ladder would have at least one acceleration acting on it. This is just one of those examples in which maths doesn't line up with reality.
@marcushendriksen8415
5 жыл бұрын
Now I think about it, this would be fun to point out in your answer in an actual exam, and to take it even further by assuming a frictionless and a uniform acceleration in the -y direction (of 9.8 m/s^2, of course)
@marcushendriksen8415
5 жыл бұрын
Hold on hold on hold on. After some actual hand-waving (in place of drawing diagrams, you see), I realized that even with an acceleration present, the ladder still shouldn't detach from the wall, at least, not until after y=0 (the ladder hits the ground.) I'm not able to explain why right now, because I don't fully know myself, but watch this space. Later - tomorrow, probably - I'll have worked it out and come back to show it.
@Wacko773
5 жыл бұрын
Can I get your email?
@gaurangagarwal3243
5 жыл бұрын
Who remember. Me ek udta sapna hoo jo aaj ban chuka hoo sach. Ab ye mera sapna hai ki sabke sapne sach me karu. Dora-e-mon.😂😂
@maxhenderson1890
4 жыл бұрын
I don’t like how in the question involving ships, it expects you to interpret that noon is “12:00”, when in fact, midday is 12.00
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