Glass of Numbers
Glass of Numbers
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Triple Integrals in Cylindrical Coordinates
Discover how to set up and evaluate a triple integral over a solid region bounded by the paraboloid y=4x^2+4z^2 and y=4 in this comprehensive Calculus 3 tutorial. I will walk you through the step-by-step process of defining the limits of integration, converting to cylindrical coordinates, and solving the integral. Perfect for students tackling advanced calculus topics, this video simplifies complex concepts with clear explanations and examples. Master the art of triple integrals and enhance your mathematical skills today.
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Переглядів: 1 704

Відео

How to set up Triple Integrals over a tetrahedron
Переглядів 7095 місяців тому
In this comprehensive tutorial, you'll learn how to set up and solve a triple integral of xyz over a solid tetrahedron. 📺 Subscribe to my channel for Math Learning! ua-cam.com/users/glassofnumbers Please help me by subscribing to my UA-cam channel. I want to use my free time to make a lot of math videos to help others and to make education available to the world. Your sharing and subscribing wi...
How to Solve Quadratic Equations by Completing the Square x^2-4x+3=0
Переглядів 2,1 тис.Рік тому
We show how to solve quadratic equations by completing the square in this video. The equation that we use to demonstrate the process is x^2-4x 3=0. Even though it is easier to solve this quadratic equation by factoring or using the quadratic formula, it is still important to learn how to use the process of completing square through solving a quadratic equation. 📺 Subscribe to my channel for Mat...
Partial Derivatives of Functions with Two and Three Variables
Переглядів 462Рік тому
This video shows how to find first partial derivatives of functions with two and three variables. We talk about examples of differentiating functions using different differentiation rules such as product rule and power rule. 📺 Subscribe to my channel for Math Learning! ua-cam.com/users/glassofnumbers Please help me by subscribing to my UA-cam channel. I want to use my free time to make a lot of...
How to Find Parametric Equations for a Tangent Line to a Curve in the Space
Переглядів 609Рік тому
This video shows you how to find parametric equations for a tangent line to a curve in the space at a given point. This is a useful skill in calculus and other areas of mathematics, and it can be used to solve a variety of problems. We will first talk about how to find the derivative of a parametric function, and use it together with the given point to find a vector equation for the tangent lin...
How to Solve Absolute Value Equation with Two Absolute Values |2x+1|=|x-3|
Переглядів 1,1 тис.Рік тому
We are showing how to solve absolute value equations with two absolute values. The equation is |2x 1|=|x-3|. The idea is to break it into four cases to solve the equation. 📺 Subscribe to my channel for Math Learning! ua-cam.com/users/glassofnumbers Please help me by subscribing to my UA-cam channel. I want to use my free time to make a lot of math videos to help others and to make education ava...
How To Solve Absolute Value Equations
Переглядів 225Рік тому
We talk about how to solve absolute value equations in this video. We have five examples in this video for absolute value equations. Each equation involves only one absolute value. 0:00 |2x-1|=3 2:36 |-2x|=8 3:40 |x 4|=0 4:53 |x 3| 4=2 8:02 5-|3x 2|=4 📺 Subscribe to my channel for Math Learning! ua-cam.com/users/glassofnumbers Please help me by subscribing to my UA-cam channel. I want to use my...
Vector Equation of Curve of Intersection of Two Spheres
Переглядів 1,2 тис.Рік тому
In this video, we talk about how to find the vector equation of curve of intersection of two spheres, x^2 y^2 z^2=4 and (x-1)^2 y^2 z^2=4. The two spheres intersect in a circle, parallel to yz-plane. We start by setting the two equations equal to each other to find the parametrization. 📺 Subscribe to my channel for Math Learning! ua-cam.com/users/glassofnumbers Please help me by subscribing to ...
Finding T, N, and B Vectors for a Helix | Helical Curve Computation Explained
Переглядів 457Рік тому
Welcome to our video on computing the T, N, and B vectors for a helix! In this tutorial, we will explore how to calculate the unit tangent, principal unit normal, and unit binormal vectors step by step. Helical curves, often resembling spirals, are not just a mathematical curiosity. They're everywhere around us, from the coils of a spring to the double helix of DNA. 0:33 - Calculating the Unit ...
How to Solve a Radical Equation with Two Square Roots
Переглядів 411Рік тому
In this video, we talk about how to solve a radical equation with two square roots. The idea is to isolate one of the square roots first and square both sides of the equation. After the first square root has disappeared, we will isolate the other square root and square both sides of the equation. 📺 Subscribe to my channel for Math Learning! ua-cam.com/users/glassofnumbers Please help me by subs...
Solving Radical Equations with One or Two Radicals
Переглядів 264Рік тому
In this video we talk about solving radical equations with one or two radicals. The general idea is to first isolate the radical, or one of the radicals, then raise both sides of the equation to the power of the radicals. 0:00 - sqrt(2x-3)=5 2:34 - x-2=sqrt(x) 9:25 - sqrt(4x-3) 3=2 vs cbrt(4x-3) 3=2 14:28 - sqrt(x) sqrt(3x 4)=6 The last example has two radicals (two square roots). The idea is t...
20 Minutes to Learn Solving Exponential Equations
Переглядів 134Рік тому
In this video we talk about solving exponential equations through five examples. 0:00 9^x = 27 1:46 4^(2x-3)=8^x 4:06 5^x/125^(3x 1)=25 8:49 3^x = 8 13:56 4^(x 3)=5^(2x) The five examples show how to manipulate the equations so that both sides have the same base. The last two examples show how to solve an exponential equation and how to do it using logarithms and natural logarithms. 📺 Subscribe...
Integral of Sqrt(e^2x + 1) dx - This one is fun!
Переглядів 1,7 тис.Рік тому
We do the integral of sqrt(e^2x 1) dx with all steps shown. This is a fun integral! We do u-subs twice, followed by partial fraction decomposition! 📺 Subscribe to my channel for Math Learning! ua-cam.com/users/glassofnumbers Please help me by subscribing to my UA-cam channel. I want to use my free time to make a lot of math videos to help others and to make education available to the world. You...
How To Find an Equation of a Plane Given a Point and Perpendicular Normal Vector
Переглядів 497Рік тому
This video explains how to find an equation of a plane given a point and perpendicular normal vector. Generally, when we want to find an equation of a plane, we need two things: 1) Point 2) Normal Vector And we have both in the given information. So, we can find a plane easily. 📺 Subscribe to my channel for Math Learning! ua-cam.com/users/glassofnumbers Please help me by subscribing to my UA-ca...
Finding the Length of a Curve in Three-Dimensional Space (e^t, sqrt(2)t, e^(-t))
Переглядів 831Рік тому
In this video we talk about finding the length of a curve in three-dimensional space. The curve is r(t) = (e^t, sqrt(2)t, e^(-t)), where t is from 0 to 2. When it comes to finding arc length, there is a square root in the integral. We talk about specifically how to deal with the integrand with the square root by recognizing the expression inside the square root is a perfect square. 📺 Subscribe ...
Graphing y=3-sqrt(x+4) using three transformations
Переглядів 296Рік тому
Graphing y=3-sqrt(x 4) using three transformations
How to Graph a Radical Function with Vertical Stretch and Shift y=3sqrt(x)-2
Переглядів 426Рік тому
How to Graph a Radical Function with Vertical Stretch and Shift y=3sqrt(x)-2
How to Graph Square Root Function with Stretch and Compression
Переглядів 983Рік тому
How to Graph Square Root Function with Stretch and Compression
Graphing Square Root Sqrt(-x-3) by Horizontal Reflection and Horizontal Shift
Переглядів 857Рік тому
Graphing Square Root Sqrt(-x-3) by Horizontal Reflection and Horizontal Shift
Graphing y=-sqrt(x)+2 using transformations
Переглядів 886Рік тому
Graphing y=-sqrt(x) 2 using transformations
How to Graph Square Root Functions with Reflections
Переглядів 943Рік тому
How to Graph Square Root Functions with Reflections
How do you write 2x-3y=6 in slope-intercept form?
Переглядів 2,6 тис.Рік тому
How do you write 2x-3y=6 in slope-intercept form?
How to Find Intercepts of Linear Equation 5y+2=3x
Переглядів 364Рік тому
How to Find Intercepts of Linear Equation 5y 2=3x
How to Find x-intercept and y-intercept of Linear Equations in Standard Form
Переглядів 1,4 тис.Рік тому
How to Find x-intercept and y-intercept of Linear Equations in Standard Form
How to Find y intercept and x intercept of a Linear Equation
Переглядів 7 тис.Рік тому
How to Find y intercept and x intercept of a Linear Equation
How to Find the Inverse of a 3x3 Matrix
Переглядів 639Рік тому
How to Find the Inverse of a 3x3 Matrix
Finding the Area of the Region Inside the Circle r=3cos(theta) & Outside the Cardioid r=1+cos(theta)
Переглядів 8 тис.Рік тому
Finding the Area of the Region Inside the Circle r=3cos(theta) & Outside the Cardioid r=1 cos(theta)
What happens when we try to find the inverse of a singular matrix?
Переглядів 488Рік тому
What happens when we try to find the inverse of a singular matrix?
How to Find the Inverse of a 2 by 2 Invertible Matrix
Переглядів 256Рік тому
How to Find the Inverse of a 2 by 2 Invertible Matrix
How to Multiply Matrices Quickly
Переглядів 308Рік тому
How to Multiply Matrices Quickly

КОМЕНТАРІ

  • @justinekyando
    @justinekyando 3 дні тому

    Your generous 😇😇😇😇❤️❤️❤️

    • @GlassofNumbers
      @GlassofNumbers 2 дні тому

      Thank you! Please help others by sharing the video 😁👍

  • @SethKadam-j7v
    @SethKadam-j7v 5 днів тому

    8:55 where did the 2 in the denominator go?

  • @SethKadam-j7v
    @SethKadam-j7v 5 днів тому

    good example

    • @GlassofNumbers
      @GlassofNumbers 2 дні тому

      Thank you! Good to hear you like the examples 😁

  • @TopGaming-cs5uv
    @TopGaming-cs5uv 7 днів тому

    i still didnt understand how to get the theta=Pi/3 value.😓

  • @thinzarkyaw6946
    @thinzarkyaw6946 7 днів тому

    your handwriting is so pretty😂

  • @promitaroychowdhury9678
    @promitaroychowdhury9678 9 днів тому

    why is the coefficient negative 3/2 in ques.2?

  • @promitaroychowdhury9678
    @promitaroychowdhury9678 9 днів тому

    why 1/2 * e^-x^2 becomes zero after subsitituing with infinity?

  • @dariaw6355
    @dariaw6355 10 днів тому

    Where did you took 4??

  • @ShreeBalaji-kg6hq
    @ShreeBalaji-kg6hq 11 днів тому

    is tanx/2 also right ?

  • @margo3320
    @margo3320 12 днів тому

    u are a life saver

  • @soph2124
    @soph2124 13 днів тому

    amazing and straightforward! I could understand everything perfectly and at the first try

  • @algeBROS-v5v
    @algeBROS-v5v 13 днів тому

    Have a doubt ! When we integrate we add a constant। term on our own?? Is this that kind of integration ?

  • @job2687
    @job2687 18 днів тому

    Thanks, amazing explanation

  • @jierongwu1955
    @jierongwu1955 18 днів тому

    Thanks for the help ❤

  • @youssefbasem9266
    @youssefbasem9266 19 днів тому

    I answered a question similar to this but it was an image to a straight line to a point instead of a plane to a pount cant belive i didnt think of taking the n as a direction vector and A as a point to a straight line 😅

    • @GlassofNumbers
      @GlassofNumbers 19 днів тому

      Similar idea! There are different ways to do this one! I think I should do a video with the question you answered 😁👍

  • @onepiece4102
    @onepiece4102 20 днів тому

    so underrated

    • @GlassofNumbers
      @GlassofNumbers 20 днів тому

      Thank you for saying that! Please help me share this video with others 😁

  • @skye-chor
    @skye-chor 21 день тому

    Thanks for being illustrative on every video you make. Love from Hong Kong

    • @GlassofNumbers
      @GlassofNumbers 20 днів тому

      Thank you! I am happy to hear that you like that style! Are you taking Calculus 3?

  • @yvettenieto4182
    @yvettenieto4182 24 дні тому

    thank you

  • @Wankateswar
    @Wankateswar 24 дні тому

    Nice sir ❤❤❤

    • @GlassofNumbers
      @GlassofNumbers 20 днів тому

      Thank you! Glad you like the video! Please help me share the video with others 😁👍

  • @carlosmontes4511
    @carlosmontes4511 26 днів тому

    thanks !!!

  • @hiiii542
    @hiiii542 27 днів тому

    thanks hon❤

  • @j10__1
    @j10__1 28 днів тому

    goat

  • @sakib4357
    @sakib4357 Місяць тому

    Your voice is heaven ♥️😩

    • @GlassofNumbers
      @GlassofNumbers 20 днів тому

      Thank you! I am happy to hear that my video helps 😁👍

  • @AbishekShah-rs6bi
    @AbishekShah-rs6bi Місяць тому

    Thank you, The trick to take make two modulus on two side are fabulous and has cleared my concept of doing this .... Thanks alot ❣️

  • @CarlAngelobalanon
    @CarlAngelobalanon Місяць тому

    Thank you

  • @Michael_Petillo
    @Michael_Petillo Місяць тому

    Wow I didn’t see to complete the square at first that makes so much more sense lol

    • @GlassofNumbers
      @GlassofNumbers Місяць тому

      Many of such problems require completing the square, and some of them are hard for us to tell. 👍

  • @xgyra
    @xgyra Місяць тому

    I got this problem and made it to where you were at 1:04. Didn't recognize that identity and went through the trouble of u-substituting sin(x) in the right half, only to lose track of my negative sign and get the wrong answer... Anyway, this helped a lot.

  • @Valgony
    @Valgony Місяць тому

    This is amazing explained every question I had

    • @GlassofNumbers
      @GlassofNumbers Місяць тому

      Great to hear that! Please help others by sharing this video!

  •  Місяць тому

    If you graph both sides, it looks like x=2 would be a solution, but that only works in the limit. With 1.9999…, the sides approximate each other.

  • @SauravSingh-f1v
    @SauravSingh-f1v Місяць тому

    👍

  • @StanleyHung
    @StanleyHung Місяць тому

    Ohhhhh so you can add as the solutions are the same and multiplying by a constant doesn't change the answer

    • @GlassofNumbers
      @GlassofNumbers Місяць тому

      When you perform the correct row operations, the solution will be the same as the original system

  • @julia_eq1
    @julia_eq1 Місяць тому

    I love you

  • @users4007
    @users4007 Місяць тому

    underrated channel

  • @Reg4JesusChrist
    @Reg4JesusChrist Місяць тому

    Flawless Presentation, Sir!

    • @GlassofNumbers
      @GlassofNumbers Місяць тому

      Thank you! Please help others by sharing the video 😁👍

  • @Reg4JesusChrist
    @Reg4JesusChrist Місяць тому

    Flawless Presentation, Sir!

    • @GlassofNumbers
      @GlassofNumbers 20 днів тому

      Thank you! Please continue to support me!!

  • @nawar6570
    @nawar6570 Місяць тому

    I didn't get it how come 3 is here? I mean how did you find the 3?

  • @Uygʻun-q2c
    @Uygʻun-q2c Місяць тому

    you saved my life

    • @GlassofNumbers
      @GlassofNumbers Місяць тому

      Glad my video helps!! Please help others by sharing the video with others 😁

  • @Vaz5107
    @Vaz5107 Місяць тому

    Bro taught me math in my second language

    • @GlassofNumbers
      @GlassofNumbers Місяць тому

      Are you taking Trigonometry now?

    • @Vaz5107
      @Vaz5107 Місяць тому

      @@GlassofNumbers Yeah

  • @austinshepherd1435
    @austinshepherd1435 2 місяці тому

    You are saving my bacon right before a Calc 3 mid term. I had a vague idea what to do but I always forget the final step. Thank You!!

  • @Tod_x
    @Tod_x 2 місяці тому

    finding gold but got platinium. Thanks edit: want to ask, does x limit need to be one number for any question?

    • @GlassofNumbers
      @GlassofNumbers 2 місяці тому

      What do you mean by one number?

    • @Tod_x
      @Tod_x 2 місяці тому

      @@GlassofNumbers I mean x only numbers, no y and z variable.

  • @offoredochie2378
    @offoredochie2378 2 місяці тому

    I think you can give a theory before the question, like explaining better what you doing, you just laying it down like my professor will, better explanation needed.

    • @GlassofNumbers
      @GlassofNumbers 2 місяці тому

      Good point, however, this is a short video not intending to replace a lecture. Explaining the theory requires a separate video. The intention for this video is to talk about how to set up the triple integral.

  • @Thepotato-mo1jh
    @Thepotato-mo1jh 2 місяці тому

    thank you so much your amazing

    • @GlassofNumbers
      @GlassofNumbers 2 місяці тому

      Thank you! Please help others by sharing this video with others!

  • @Bryan-l2o
    @Bryan-l2o 2 місяці тому

    my proffessor sucks in my calc 2 class i can barely understand bro

    • @GlassofNumbers
      @GlassofNumbers 2 місяці тому

      I hope you are getting better at this!

  • @Bryan-l2o
    @Bryan-l2o 2 місяці тому

    ilysm

  • @Bryan-l2o
    @Bryan-l2o 2 місяці тому

    ilysm

  • @lilyshaalan1290
    @lilyshaalan1290 2 місяці тому

    Your so smart thank you

  • @timyolol
    @timyolol 2 місяці тому

    how would you do this but for a general plane instead of the xz-plane

  • @deronhogans1786
    @deronhogans1786 2 місяці тому

    Couple years later from you posting this it really helped me to understand why I need 2 integrals

    • @GlassofNumbers
      @GlassofNumbers 2 місяці тому

      Thank you! Please help me by sharing the video with others 👍😁

  • @kariukiwangari907
    @kariukiwangari907 2 місяці тому

    Thanks, bro. This video has really helped me. I'm struggling with my maths course, but your explanation has renewed my hopes that I may pursue it after all. I was toying with the thought of dropping the course, but not anymore. I'll fight through it, and I'll come out on top. Thanks a ton.

    • @GlassofNumbers
      @GlassofNumbers 2 місяці тому

      Good to hear that! Wish you the best in your math courses!!

  • @maleeshapriyanjana7604
    @maleeshapriyanjana7604 2 місяці тому

    Thanks a lot. I was struggling a lot to solve the last art

    • @GlassofNumbers
      @GlassofNumbers 2 місяці тому

      Good to hear that! Please help others as well by sharing the video 😁👍