Duyệt các ví dụ hoạt ảnh Calculus được tuyển chọn trong Math, bao gồm các cảnh Manim có thể tái sử dụng, chứng minh trực quan và ý tưởng sẵn sàng để giảng dạy.
Math · 5 hoạt ảnh
This animation visualizes the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ... by repeatedly halving a unit square. Each term is shown as a filled rectangle that fits beside the previous ones like puzzle pieces, and the partial sums are displayed numerically, all converging toward the limit of 2.
Visualizes the chain rule through three stacked number lines representing the input x, the intermediate value g(x), and the output f(g(x)). Animated small changes Δx propagate through the composition, making the multiplicative structure of the chain rule visually intuitive.
Builds intuition for the derivative by animating the limit definition. A secant line between two points on f(x) = x² is drawn and animated as h approaches 0, visually converging to the tangent line. The difference quotient formula transforms into the derivative formula.
Visualizes how Riemann sums approximate the definite integral by increasing the number of rectangles under f(x) = x² from 0 to 3. As n grows from 4 to 32, the approximation converges to the exact area of 9, illustrating the limit definition of the integral.
Demonstrates how the Taylor series builds increasingly accurate polynomial approximations of cos(x) around x=0 by successively adding terms. Each new term is animated in a new color, revealing how the approximation extends further from the center.
