=U+Pv

Freedom of speech is a right, but it must never infringe upon others’ freedom, nor should it be used as a means for one person to retaliate against another!

[=U+Pv @include1010]

Today we'll tackle a classic parabola tangent line problem!
Given the curve y² = 4px, find the equation of its tangent line at point P(x₀, y₀).
The step-by-step derivation is super clear; I recommend saving it! Where do you usually get stuck when solving these kinds of problems?
#parabolatangentline #analyticgeometry #highschoolmathematics

[=U+Pv @include1010]

Master the core knowledge of regular polygons! The number of sides determines everything; interior and exterior angles are supplementary at 180°; the sum of exterior angles is 360°. A pentagon's exterior angle is 72°, and a hexagon's interior angle is 120°. One diagram to solve geometric calculations and easily tackle math problems!

#RegularPolygons #InteriorAndExteriorAngles #GeometricFormulas

[=U+Pv @include1010]

Includes limits of core functions to help you quickly master the essence of calculus.

#Limits #CalculusTools #Mathematics

[Mathematica @mathemetica]

This reference table pairs graphs with standard integral formulas:

>Area bounded by x-axis: Area = ∫_b^a f(x) dx
>Area bounded by y-axis: Area = ∫_c^d f(y) dy
>Area between two curves: Area = ∫_b^a [f(x) − g(x)] dx
>Volume of revolution about x-axis (disk method): Volume = π ∫_b^a y² dx
>Volume of revolution about y-axis (disk method): Volume = π ∫_c^d x² dx

Real-life applications: These formulas are used to calculate total accumulated quantities such as distance traveled from velocity curves, enclosed regions in economics and biology, and volumes of three-dimensional objects like tanks, pipes, vases, and machine parts in engineering and manufacturing.

[=U+Pv @include1010]

@mathemetica A new perspective: In AI training, we use a method similar to "area of ​​curve" to accumulate gradients and optimize loss, just like accumulating knowledge through integration.

[Learn with Sam @Sam_Axiom]

Thermodynamics Formula Sheet.

Part -1

[=U+Pv @include1010]

Thermodynamic formula tables are incredibly useful! However, in practical engineering, deviations in real gas conditions are often overlooked—after correction using the van der Waals equations, efficiency predictions become much more accurate. What non-ideal situations have you encountered recently?

[=U+Pv @include1010]

@WHLeavitt A! Extreme racism must be eradicated; it poses a major threat to human civilization!

[Math Files @Math_files]

https://t.co/igw5eCM254

[=U+Pv @include1010]

@Math_files This incredibly simple and beautiful proof always reminds me of the harmonic oscillator wave function in quantum mechanics—π emerges naturally from the "dimensional increase." Does anyone know of any other hidden integrals of π? Feel free to share!

[=U+Pv @include1010]

@liuyuxin89064 Do you have a better way?

[=U+Pv @include1010]

Mathematical magic? Taylor series perfectly approximates sin(x) using polynomials! Linear to quintic, the more terms, the more accurate!

#TaylorSeries #FunctionApproximation #MathematicalModeling

[=U+Pv @include1010]

@IgnoredReal Chinese women nowadays prefer African men.

[=U+Pv @include1010]

Polynomial addition and subtraction!
Align coefficients for instant calculation!

#Algebraicoperations #Polynomialadditionandsubtraction #Mathpractice

[=U+Pv @include1010]

@ghostonki There is no doubt that China is already a truly developed country.

[Math Files @Math_files]

Gabriel's Horn, where a surface can have Infinite surface area but finite surface volume.

[=U+Pv @include1010]

@Math_files Gabriel's Horn is so captivating: a finite volume with an infinite surface area, perfectly embodying the idea of ​​"infinite effort, finite reward." In reality, would you choose to "fill in" or "paint"?

[=U+Pv @include1010]

@shine_gomiseifu I think you are Chinese.

[=U+Pv @include1010]

@daily_da1 Remember to visit Chengdu and Chongqing next time.

[=U+Pv @include1010]

@thedantelord Smartwatches? I still prefer mechanical watches.

[=U+Pv @include1010]

@arkuy99 Chinese people saw it...