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How Mathematicians Skip Hard Integrals and Use Squeeze Theorem (limit of arc length on y=x^n)

22K views · 1d ago · 14:52

3Blue1Brown • Ahmad syafi • Allison Lamery • Angel Avila • Anthony Hunting • Anyway • Ben Delo • bontle sjm • Cameron Quinn • charlie lewinski • Corey Rufener • David I Miller • Doc Ockey • exchsac • Glenn X • Gramps • Hayden S • huguens nevelus • Jake Albert • jappiesaus • Jessica • Joel Wong • Johan Renko • Karl Tang-Wang • Manil Trivedi • Mark Pagura • MarkM • Mas • Matt • Matthias Beeler • Michael ZHOU • Michelle Liang • Mizel Cluett • Nerd • Nicolai Lilly • Paul Lyon •…

▶️ Mentioned videos: Arc length formula

Can you solve this Bessel's Differential Equation? x^2y''+xy'+(x^2-1/4)y=0

19K views · 2d ago · 22:49

Hearing the words Bessel differential equation is enough to make most advanced calculus students close their textbooks in panic. We are conditioned to believe that these equations can only be solved using infinite power series with recurrence relations. However, when the order is precisely one-half, the entire structure simplifies into something wonderfully manageable. Here is the elegant substitution that reveals an explicit, closed-form solution with ultimate satisfaction.

Disc Method or Shell Method? The Secret to Rotating y = sin(x^2)

17K views · 5d ago · 8:28

When calculating volumes of solids of revolution, student frustration rarely comes from setting up the integral—it comes from getting trapped in an integral you cannot solve. Rotating y=sin(x^2) about the x-axis forces you into the disc method and an unmanageable integrand. But rotating about the y-axis introduces the cylindrical shell method, where dx integration creates the perfect setup for u = x^2.

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Can we solve a quadratic equation using logarithm?

118K views · 12d ago · 6:10

I have been trying to use logarithms to solve a quadratic equation, but no success so far! 3Blue1Brown • Ahmad syafi • Allison Lamery • Angel Avila • Anthony Hunting • Anyway • Ben Delo • bontle sjm • Cameron Quinn • charlie lewinski • Corey Rufener • David I Miller • Doc Ockey • exchsac • Glenn X • Gramps • Hayden S • huguens nevelus • Jake Albert • jappiesaus • Jessica • Joel Wong • Johan Renko • Karl Tang-Wang • Manil Trivedi • Mark Pagura • MarkM • Mas • Matt • Matthias…

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I can "prove" 1=2 without dividing by 0

55K views · 17d ago · 8:24

We will see a "false proof" of 1=2. Enjoy! How to prove cos(a-b)=cos(a)cos(b)+sin(a)sin(b) geometrically 3Blue1Brown • Allison Lamery • Anthony Hunting • Anyway • Ben Delo • Caoimhe Seymour • charlie lewinski • Corey Rufener • CTAR • David I Miller • Doc Ockey • exchsac • Gramps • Hayden S • huguens nevelus • jappiesaus • Jessica • Johan Renko • Karl Tang-Wang • Manil Trivedi • Mark Pagura • MarkM • Mas • Michael ZHOU • Michelle Liang • Mister Hardware • Mizel Cluett • Nerd…

▶️ Mentioned videos: How to prove cos(a-b) cos(a)cos(b) sin(a)sin(b) geometrically

Factoring 100 Polynomials In One Take!

33K views · 21d ago · 3:57:54

We will factor 100 polynomials in one take! These problems are designed for Algebra, Precalculus, and Calculus students, and we go through every key technique from factoring the greatest common factors, trinomials, and special products (difference of squares, sum/difference of cubes) to advanced methods like factoring by grouping, synthetic division, substitution, quartic equations, and Sophie Germain’s Identity.

Topics: 100 polynomial factoring problems

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Challenge: 10 rational function problems

26K views · 1mo ago · 1:08:54

Q1, 00:25, can a rational function have domain and range of all real numbers? Q2, 03:03, constructing a rational function with asymptotes holes and intercepts Q3, 08:54, rational function rate word problem (pipes filling a tank) Q4, 14:21, finding the inverse of a rational function Q5, 20:41, partial fraction decomposition Heaviside cover up method Q6, 27:01, solving functional equations with rational inputs Q7, 32:51, crossing horizontal asymptotes and finding range…

Topics: 10 rational function problems

If y^y=x, then dy/dx=? (ft. Lambert W function)

34K views · 1mo ago · 4:16

We will find the derivative of y^y=x and will also use the Lambert W function to simplify the final result. This channel is dedicated to sharing the fun of mathematics and inspiring students around the world.

When calculus teacher struggles with BASIC multiplication

135K views · 1mo ago · 1:41

▶️ Mentioned videos: Video on youtube.com

How to set up optimization problems (20 common calculus 1 questions)

26K views · 1mo ago · 1:37:32

Most students don't fail optimization on the calculus, they fail on the setup. Translating word problems into a single, solvable function is the ultimate bottleneck in Calculus 1. I worked through 20 optimization problems to cover every primary setup pattern you will encounter on an exam: 1. Distance minimization 2.Area and perimeter constraints 3.Cost and revenue optimization 4.Trigonometric setup models

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Precalculus Practice Tests #2: Polynomial & Rational Function

17K views · 1mo ago · 1:22:10

This channel is dedicated to sharing the fun of mathematics and inspiring students around the world. 3Blue1Brown • Allison Lamery • Anthony Hunting • Anyway • Ben Delo • Caoimhe Seymour • charlie lewinski • Corey Rufener • CTAR • David I Miller • Doc Ockey • exchsac • Gramps • Hayden S • huguens nevelus • jappiesaus • Jessica • Johan Renko • Karl Tang-Wang • Manil Trivedi • Mark Pagura • MarkM • Mas • Michael ZHOU • Michelle Liang • Mister Hardware • Mizel Cluett • Nerd •…

Topics: Precalculus practice test #2 · Q1, vertical asymptotes and holes · Q2, rational root theorem · Q3, domain and range with a hole · Q4, end behavior of polynomials · Q5, constructing polynomials from zeros

Is (x+y)^4=x^4+y^4 ever true?

63K views · 1mo ago · 6:50

Every math student learns early on that distributed exponents are a mathematical sin. While the identity fails completely for non-zero real numbers, complex numbers follow an entirely different set of rules. Expanding the binomial and factoring out trivial cases reveals a rich geometric relationship in the complex plane. Take a closer look at why a classic algebra mistake is secretly a gateway to complex algebra.

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Precalculus Practice Tests #1: Functions & Transformations

21K views · 1mo ago · 1:24:23

A 20-question practice test with complete step-by-step video solutions, designed for AP Precalculus, High School, and College Precalculus students. Topics Covered in Practice Test #1 Domain and range Difference quotients Function composition Graph transformations Average rate of change Inverse functions

Topics: Precalculus Practice Test #1 · Q1, Domain and Range from Graph · Q2, Range of f(x) = 3 - |x + 2 · Q3, Difference Quotient for f(x) = 3x2 - 2x + 1 · Q4, Average Rate of Change of f(x) = x3 - 2x on [1, 1+h] · Q5, Domain of Composite Function (f ∘ g)(x)

When (ln(x))^x = 2 has NO closed-form solution...

50K views · 1mo ago · 7:42

We will see how to use Newton's method to approximate the root of the equation (ln(x))^x=2. This channel is dedicated to sharing the fun of mathematics and inspiring students around the world.

Topics: Solving (ln(x))^x=2 using Newton's Method · Proof of the Newton's Method

10 First-Order Differential Equations to Master Before Your Exam

41K views · 1mo ago · 1:19:18

Master first-order differential equations step-by-step. These 10 questions include all the topics you have know such as separable, linear, homogenous, exact, almost exact, integrating factor, Bernoulli, Clairaut, and Riccati.

Topics: 10 Essential First-Order Differential Equations · Q1: Separable Differential Equation · Q2: Exact Differential Equation · Q3: Bernoulli Differential Equation · Q4: Integrating Factor IVP · Q5: Non-Linear Substitution

📖 Mentioned book: Apparel & Shirts

▶️ Mentioned videos: First-Diff Eqs Ultimate Summary

100 Trig Identities: The Ultimate 5-Hour Math Marathon

100K views · 2mo ago · 5:01:13

100 trig identities. 5 hours. One take. Master the complete foundation of precalculus and calculus. From fundamental Pythagorean identities to Calculus 2 "integral-ready" forms, every essential expression is solved step-by-step.

Topics: , Finally, 100 trig identities in one take!

📖 Mentioned book: Math T-Shirts & Apparel

▶️ Mentioned videos: Video on youtube.com

10 derivative questions that differentiate experts from beginners

53K views · 2mo ago · 1:02:18

Can you solve all 10 of these derivative calculus questions? In this video, we go from tricky standard differentiation rules to advanced conceptual problems involving functional equations, non-differentiable products, parametric self-intersections, and definition of the derivative proofs.

Topics: 10 derivative challenging problems

10 Factoring Problems That Separate Experts From Beginners

74K views · 2mo ago · 59:40

10 factoring problems engineered to separate standard textbook execution from true mastery. Key techniques covered Sophie Germain's Identity Synthetic Division & Quartic Factoring Algebraic Substitution Double-Cross Method

Topics: Q1: x^4 + 64y^4 · Q2: x^5 + 3x^4 - 23x^3 - 27x^2 + 166x - 120 · Q3: x^4 - 4x^3 + 12x^2 - 16x + 15 · Q4: x^4 + 2026x^2 + 2025x + 2026 · Q5: (x-a)(x-2a)(x-3a)(x-4a) + a^4 · Q6: x^8 - 3x^6 + 4x^4 - 3x^2 + 1

How to get 1/2 of a cylinder?

67K views · 2mo ago · 6:12

This channel is dedicated to sharing the fun of mathematics and inspiring students around the world. 3Blue1Brown • Allison Lamery • Anthony Hunting • Anyway • Ben Delo • Caoimhe Seymour • charlie lewinski • Corey Rufener • CTAR • David I Miller • Doc Ockey • exchsac • Gramps • Hayden S • huguens nevelus • jappiesaus • Jessica • Johan Renko • Karl Tang-Wang • Manil Trivedi • Mark Pagura • MarkM • Mas • Michael ZHOU • Michelle Liang • Mister Hardware • Mizel Cluett • Nerd •…

▶️ Mentioned videos: Want more integrals? 100 integral video

10 trigonometric equations that separate EXPERTS from beginners

63K views · 2mo ago · 54:34

Master trigonometric equations, inverse trig functions, and identity tricks with these 10 essential practice problems! In this math tutorial, we work through step-by-step solutions to popular calculus readiness, precalculus, and math competition problems, covering nested functions, infinite geometric series, and graphical intersections. This is a perfect practice or challenge for your precalculus class. Enjoy!

10 quadratic equations that separate experts from beginners

120K views · 2mo ago · 51:52

Proving the quadratic formula by using Euler’s formula This channel is dedicated to sharing the fun of mathematics and inspiring students around the world. 3Blue1Brown • Allison Lamery • Anthony Hunting • Anyway • Ben Delo • Caoimhe Seymour • charlie lewinski • Corey Rufener • CTAR • David I Miller • Doc Ockey • exchsac • Gramps • Hayden S • huguens nevelus • jappiesaus • Jessica • Johan Renko • Karl Tang-Wang • Manil Trivedi • Mark Pagura • MarkM • Mas • Michael ZHOU •…

Topics: 10 expert-level quadratic equation questions · Q1: Finding range of 'a' for specific real solutions · Q2: Proving the Quadratic Formula (Completing the Square) · Q3: Finding 'k' for a common root for two quadratic equations · Q4: Computing alpha^3 + beta^3 (Vieta's Theorem) · Q5: Solving a quartic equation using quadratic methods

▶️ Mentioned videos: Proving the quadratic formula by using Euler’s formula

Solving a rational equation by "completing the square"

53K views · 2mo ago · 7:43

Google Gemini gave me this rational equation x^2+(x/(x+1))^2=3 and showed me how nicely designed this equation because it could be done with "completing the square" in a special way! This channel is dedicated to sharing the fun of mathematics and inspiring students around the world.

The triangle is 1/2 of a rectangle so why is the cone 1/3 of a cylinder?

182K views · 2mo ago · 7:45

We will see why the volume of a cone is 1/3 of the cylinder with the same base and height. First we will do a "water proof", then we will see how to use the disk method to compute the volume of the revolution of the solid. Great lesson for calculus 1 and AP calculus students.

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Limit of x^(y^z) as (x, y, z) goes to (0, 0, 0)

27K views · 3mo ago · 10:36

Let's invest the multivariable limit of x^y^z as (x, y, z) goes to (0, 0, 0).

📖 Mentioned book: Shop math t-shirts & hoodies