LearnPlaySolve
LearnPlaySolve
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A Calculus Optimization Problem
A Calculus Optimization Problem
Переглядів: 1 688

Відео

Descartes & The Fly
Переглядів 9 тис.Рік тому
Descartes & The Fly
What's the Largest Ball You Can Fit In A Parabolic Vase?
Переглядів 856Рік тому
What's the Largest Ball You Can Fit In A Parabolic Vase?
A Wheely Fun Geometry Problem 2
Переглядів 263Рік тому
A Wheely Fun Geometry Problem 2
Gabriel's Horn & The Painter's Paradox
Переглядів 7 тис.Рік тому
Gabriel's Horn & The Painter's Paradox
The Napkin Ring Paradox
Переглядів 1,1 тис.Рік тому
The Napkin Ring Paradox
Can You Make Any Number Using Exactly 4 Fours?
Переглядів 1,1 тис.Рік тому
Can You Make Any Number Using Exactly 4 Fours?
or What's the Nth Fibonacci Number?
Переглядів 475Рік тому
or What's the Nth Fibonacci Number?
Maximizing Volume: A Calculus Problem
Переглядів 641Рік тому
Maximizing Volume: A Calculus Problem
The Power of Exponentials: Two Demonstrations
Переглядів 6212 роки тому
The Power of Exponentials: Two Demonstrations
Related Rates: A Calculus Problem
Переглядів 2 тис.2 роки тому
Related Rates: A Calculus Problem
Projectile Motion: A Vector Calculus Problem
Переглядів 11 тис.2 роки тому
Projectile Motion: A Vector Calculus Problem
Breaking the Cycloid: A Geometry Problem
Переглядів 22 тис.2 роки тому
Breaking the Cycloid: A Geometry Problem
The Tractrix: A Calculus Problem
Переглядів 4,9 тис.2 роки тому
The Tractrix: A Calculus Problem
The Four Ants: A Calculus Problem
Переглядів 6 тис.2 роки тому
The Four Ants: A Calculus Problem
The Belt-Around-the-Earth Problem
Переглядів 1,6 тис.2 роки тому
The Belt-Around-the-Earth Problem
Logarithm & Blues: An Introduction to Logs
Переглядів 1,1 тис.3 роки тому
Logarithm & Blues: An Introduction to Logs
A Wheely Fun Geometry Problem
Переглядів 1,8 тис.4 роки тому
A Wheely Fun Geometry Problem
Is This Equation Proof of God?
Переглядів 5 тис.4 роки тому
Is This Equation Proof of God?
Which is Greater? A Calculus Problem
Переглядів 1,5 тис.4 роки тому
Which is Greater? A Calculus Problem
The Deadliest Proof in Mathematics
Переглядів 11 тис.4 роки тому
The Deadliest Proof in Mathematics
What's the Volume of a Donut? Calculus
Переглядів 29 тис.4 роки тому
What's the Volume of a Donut? Calculus
A Quick Proof of the Pythagorean Theorem
Переглядів 9964 роки тому
A Quick Proof of the Pythagorean Theorem
The Catenary: A Vector Calculus Problem
Переглядів 10 тис.4 роки тому
The Catenary: A Vector Calculus Problem
Can You Find These 2 Numbers?
Переглядів 4974 роки тому
Can You Find These 2 Numbers?

КОМЕНТАРІ

  • @dragonlovesdiamond9512
    @dragonlovesdiamond9512 5 місяців тому

    Im confused why the arc length of the circle = the = x+a

  • @ManuelGPython
    @ManuelGPython 5 місяців тому

    Buen vídeo. ua-cam.com/video/co23oGDaH5k/v-deo.html

  • @ziaulhaq3066
    @ziaulhaq3066 6 місяців тому

    Good yar!! Very nice animation and explanation

  • @bountyonwii1087
    @bountyonwii1087 6 місяців тому

    Nice video, but i don’t understand What we have : 2 pi […] sqrt 1+ (-1/x**2)**2. At the start for the surface.

    • @LearnPlaySolve
      @LearnPlaySolve 6 місяців тому

      I'm sorry, I wish I understood your question. Would you mind restating it?

  • @Testjohnny551
    @Testjohnny551 6 місяців тому

    thanks for the video

  • @maxpercer7119
    @maxpercer7119 6 місяців тому

    this is a birds eye view, or 'from above' view

  • @samueldeandrade8535
    @samueldeandrade8535 6 місяців тому

    Oh wow! This channel looks GREAT!!! Funny thing: I clicked on the video thinking the guys in the thumbnail were carrying a sofa. Hahahahahaha. So I was expecting to see something about the Sofa Problem and was confused because if that was the case, there is some Calculus there, but it is not a purely Calculus problem, whatever my mind means by that. Instead the video is about a particular case of the Sofa Problem. Very cool.

  • @pace_18
    @pace_18 6 місяців тому

    Amazing video

  • @Greaterthantheproduct
    @Greaterthantheproduct 6 місяців тому

    AP tests near, As I shed a tear, This Video reminded me That I’m screwed

    • @8ball708
      @8ball708 6 місяців тому

      This is much harder than anything that would be on the AP calc exam

  • @arlo2150
    @arlo2150 6 місяців тому

    I’m confused as to why the derivative when 0 determines the length

    • @LearnPlaySolve
      @LearnPlaySolve 6 місяців тому

      When the derivative is zero, the original function is either at a maximum or minimum. This is the basis for optimization problems. By setting the derivative to zero, we found the optimal length given the restraints of the problem. I explain the process in more detail in this video: ua-cam.com/video/JsiNBfcB2rg/v-deo.htmlsi=t09SSEvFGQHXSv_k

  • @mrdraw2087
    @mrdraw2087 6 місяців тому

    Up and Atom had a similar video a while ago, although less mathematical.

  • @gonendraverma10
    @gonendraverma10 6 місяців тому

    Sir, Please provide another link in description for understanding integral formulas of surface area and volume. Video was really amazing and I learned a new point of view to observe things. 🙏🙏🙏🙏🙏🙏

  • @user-rm5md2do6d
    @user-rm5md2do6d 6 місяців тому

    You forgot g...

  • @Caio_Myguel
    @Caio_Myguel 6 місяців тому

    If the starting and ending position are at the same level, then complementary angles will reach the same ending position.

  • @bonfacemuthuri9840
    @bonfacemuthuri9840 7 місяців тому

    Thanks you are the best

  • @matr1x_glitch
    @matr1x_glitch 7 місяців тому

    I SAY WE MAKE DONUTS SQUARESSSSSSS

  • @matr1x_glitch
    @matr1x_glitch 7 місяців тому

    Ya know what ya should be, a teacher, might actually help fix the fu🎉🎉in education system for once and maybe people could learn

  • @matr1x_glitch
    @matr1x_glitch 7 місяців тому

    Wow, actually learned something, my math teacher could never-

  • @not_dfskjske
    @not_dfskjske 7 місяців тому

    The only reason im here is because in my math class you were my substitute teacher 😅

  • @abacaabaca8131
    @abacaabaca8131 7 місяців тому

    Thanks to this video I was able to draw cycloid in code. I want the computer to slowly draw the cycloid. Before this, I just prepare all the coordinates before hand in a data structure before drawing them i.e using factory method. But it draws the cycloid but not draw it slowly. What I need to do is that: angle+=1.0f*fElapsedTime; Then update x and y coordinate And draw using those.

  • @ruenjou
    @ruenjou 7 місяців тому

    Liked the presentation. The amount of details is just right.

  • @RaulLopez-rq6wh
    @RaulLopez-rq6wh 7 місяців тому

    How could you calculate the point new position in the x.y plane if the circle rotates in place?

    • @LearnPlaySolve
      @LearnPlaySolve 7 місяців тому

      The circle does not rotate in place. It rolls along a straight line.

    • @RaulLopez-rq6wh
      @RaulLopez-rq6wh 7 місяців тому

      @@LearnPlaySolve sorry, I meant an hypothetical scenario where it rotates in place, or do you mean it gets calculated the same?

    • @LearnPlaySolve
      @LearnPlaySolve 7 місяців тому

      Then I suppose you could just treat it like a unit circle. Every point could be defined as (cosx,sinx).

  • @thonloai
    @thonloai 7 місяців тому

    dat ...so cool

  • @Spyder6898
    @Spyder6898 7 місяців тому

    The assumption that 1/infinity is zero is the flaw. 1/infinity APPROACHES zero but never gets there. Therefore you never actually get the volume exact either. Conundrum solved. You’re welcome.

    • @LearnPlaySolve
      @LearnPlaySolve 7 місяців тому

      Calculus is based on limits. It should already be understood that 1/infinity approaches zero. Saying "1/infinity is zero" is just a shorthand way of saying that. There's a formal definition and a practical definition. I always tell calculus students to think of zero and infinity as reciprocals of each other. 1/zero is infinity, and 1/infinity is zero. Even though that's not technically true, it definitely leads to a more intuitive understanding.

    • @machine-boy
      @machine-boy 6 місяців тому

      You are correct, 1/∞ is ε However, I do not care because it does not get me anywhere neither in practical nor pure mathematics

  • @charlesharrison4077
    @charlesharrison4077 7 місяців тому

    Let’s bring in our old friend the super task and knock this job out and head to lunch. :)

  • @runekingthor5958
    @runekingthor5958 7 місяців тому

    You Are Most the Underrated youtube i Ever Seen You really explained Jee advance Level Concept In Simple word You Got My Sub Bro❤ A lot Of Love from 🇮🇳India

    • @LearnPlaySolve
      @LearnPlaySolve 7 місяців тому

      Thank you so much! That means a lot. I have another calculus video coming very soon. 😃

  • @leexavier44
    @leexavier44 7 місяців тому

    Great learning experience thank you

  • @Mcolive123
    @Mcolive123 8 місяців тому

    This is the best solution I have ever seen for this for this problem, keep up the amazing work!!! Greetings from Turkey ✌🏻✌🏻

    • @LearnPlaySolve
      @LearnPlaySolve 8 місяців тому

      Wow, thank you for those kind words! 😃

  • @minatonamikaze2637
    @minatonamikaze2637 8 місяців тому

    Damn, just imagine how genius he was🤯

  • @jasonbenjamin2560
    @jasonbenjamin2560 8 місяців тому

    W sub for my 3rd period

  • @JfjfDjdhd
    @JfjfDjdhd 8 місяців тому

    W sub teacher

  • @Cqrt3r
    @Cqrt3r 8 місяців тому

    holy fuck

  • @AJ-et3vf
    @AJ-et3vf 8 місяців тому

    The integration part went too long because you didn't use hyperbolic identities, but if you used it, the proof would've been so much shorter than otherwise!!!!

    • @LearnPlaySolve
      @LearnPlaySolve 8 місяців тому

      That is true. But my goal wasn't to do it quickly. It was to demonstrate calculus concepts and integration techniques. I appreciate your advice. In the future, I hope to make a video about the hyperbolic trigonometric functions and identities.

  • @Mike-ks6qu
    @Mike-ks6qu 9 місяців тому

    Wow. This is so much easier with calculus. Im in a calc based physics class, and we aren't using calc. Just algebra. This makes way more sense to me.

  • @scienceandtech4497
    @scienceandtech4497 9 місяців тому

    Interesting 😂

  • @scienceandtech4497
    @scienceandtech4497 9 місяців тому

    This was amazing

  • @Ovoparity-jh6bt
    @Ovoparity-jh6bt 9 місяців тому

    Fun fact:although the volume is π it is impossible to fill as it would never get the the bottom

    • @Ovoparity-jh6bt
      @Ovoparity-jh6bt 8 місяців тому

      The paint would eventually reach terminal velocity and would not get faster but as the horn is infinitely long it cannot reach the end of it technically yes you could have enough paint to do it but it would be impossible for the paint to reach the end

  • @thickmomson
    @thickmomson 9 місяців тому

    Underrated af

  • @mihaleben6051
    @mihaleben6051 9 місяців тому

    It was a triangle.

  • @ebrahimudaipurwala3753
    @ebrahimudaipurwala3753 9 місяців тому

    I was working with tori for a math paper and I must say I have not found a derivation that is this well explained! Kudos 👏

  • @barnabasonubi336
    @barnabasonubi336 10 місяців тому

    I have 3 questions. 1) What changes do we have to make for a difference in height of target and cannon? 2) What adjustment would we have to make for a cannon ball of different mass? 3) how do we calculate the magnitude using something like a rubber band setup?

    • @suspended3785
      @suspended3785 9 місяців тому

      I don't think the mass of cannon ball matters as the value of gravitation acceleration is constant for all masses

    • @barnabasonubi336
      @barnabasonubi336 9 місяців тому

      @@suspended3785 surely a cannon with a constant propelling force won't propel a projectile with heavier mass as far as it will propel a projectile with a relatively lighter mass. I think that with the force constant, the velocity of the lighter ball will be higher than that of the heavier ball.

    • @suspended3785
      @suspended3785 9 місяців тому

      @@barnabasonubi336 This will be the case if you are not neglecting air resistance, drag etc. If those are neglected (like in this video) the mass of ball would not matter on the distance. Only the initial velocity matters. Ps. The range of any projectile is given by R = u²sin(2X)/g where u is the initial velocity and x is the angle in degrees and g is gravitational acceleration.

    • @barnabasonubi336
      @barnabasonubi336 9 місяців тому

      @@suspended3785 Is there a way I can share a video of this experiment with you, so you see what I'm saying? What I'm using is a catapult setup

    • @suspended3785
      @suspended3785 9 місяців тому

      @@barnabasonubi336 upload it on UA-cam

  • @amirkefiraltroterminator2556
    @amirkefiraltroterminator2556 10 місяців тому

    16:00 really?!

  • @arturo.1895
    @arturo.1895 10 місяців тому

    I just didn't understand why x+a is the same as the arc length of the circle. 2:31

    • @konoveldorada5990
      @konoveldorada5990 10 місяців тому

      Same bro

    • @LearnPlaySolve
      @LearnPlaySolve 10 місяців тому

      You could take that line segment (x+a) and wrap it along the circle, it would equal that specific arc length. We know this because the circle rolled along that same line segment without slipping

    • @arturo.1895
      @arturo.1895 10 місяців тому

      ​@@LearnPlaySolveyeah, so since the circle rolled without slipping, all of its points touched the line, forming a segment which is, by definition, is the arc length.

  • @veronicalin2492
    @veronicalin2492 10 місяців тому

    why x=rsin theata not rcos?

    • @LearnPlaySolve
      @LearnPlaySolve 10 місяців тому

      Either one would work. I just like to end up with a positive derivative.

  • @igorjasenovski4313
    @igorjasenovski4313 10 місяців тому

    You did a greate job on this video and explanação!!!

  • @rudebaster4562
    @rudebaster4562 10 місяців тому

    Why is there a phi in next to the intergral at 01:23 (my friend ask me[were at the debate situation])

    • @LearnPlaySolve
      @LearnPlaySolve 10 місяців тому

      That's the formula for the volume of a solid of revolution. When integrating solids of revolution, you are essentially adding up an infinite number of circles (or infinitely thin cylinders). The area of a circle is πr^2, so it makes sense that their sum would also contain π. When you factor the π all the way out of the integral, that's the formula you get.

  • @boeroeng4182
    @boeroeng4182 10 місяців тому

    Thank you, trying to calculate the parabola for a shell in my game not irl thank you

  • @r.guerreiro140
    @r.guerreiro140 10 місяців тому

    Thank you :)

  • @existentialist77
    @existentialist77 11 місяців тому

    this is the clearest explanation by far

  • @zenmonk29
    @zenmonk29 Рік тому

    great video man