Showing 12 results
Related Rates Visualizer
Related rates visualization using implicit chain rule integration with respect to time (dt). Demonstrates the geometric parameter shift paradox of Constant dV/dt impacting spherical radii and conical fill heights dynamically.
MVT & Rolle's Explorer
MVT interactive module letting users sweep endpoints to compute the secant, subsequently automatically identifying all internal $c$ points where tangent perfectly parallels secant. Built with Rolle's edge case and cusp logic breakers.
Riemann Sum Approx
Interactive summation explorer comparing Left, Right, Midpoint Riemann sums and Trapezoidal logic. N-slider rapidly expands bounding box series $\Sigma$ into exact integral space via $N \rightarrow \infty$, dynamically revealing errors algebraically and geometrically.
FTC Accumulation
Fundamental Theorem of Calculus visually represented. Sweeps across $f(t)$ bounds bridging dynamic differential area accumulation natively into the $F(x)$ graphing engine.
Solid of Revolution Volume
Volumetric solids of revolution visualizer computing the Washer Method natively via integral bounds. Calculates both standard axis limits and offset axis shifts dynamically.
Slope Field Explorer
Slope field generator plotting directional isoclines. Includes an interactive differential Euler-trace mechanism resolving specific math solutions when a distinct Initial Condition point is dropped onto the coordinate grid.
Integration by Parts
Integration by parts geometric derivation visualizing the separation of total paramteric bounding box $uv$ into constituent sub-integrals $\int v du$ and $\int u dv$ via animated slicing logic.
Improper Integrals Explorer
Improper integrals interactive limit testing. Visually computes limit convergence against infinity comparing $1/x$, $1/x^2$, and $e^{-x}$ behavior with dynamic auto-zooming coordinate geometries.
Logistic Growth Differential Eq
Differential logistic population map visualizing the $dP/dt = kP(1 - P/K)$ growth carrying capacity asymptote model. Sweeps dynamic background slopefields evaluating inflection velocity shifts mathematically derived from Partial Fractions.
Euler's Method Explorer
Iterative numeric sequence plotting Euler's method vs True Analytical Solution paths. Modifying the $\Delta x$ subdivision actively updates truncation error margins mapping concave dynamics across polynomial and sinusoidal shift patterns.
Parametric Motion Vectors
Parametric Cartesian vector tracking framework decoupling $x$ and $y$ positional derivatives. Casts independent $\langle dx/dt, dy/dt \rangle$ vectors against the path map to visualize orthogonal component logic and resulting chain rule geometry.
Polar Curves & Area
Polar geometry visualizer tracking rotational $r(\theta)$ traces. Highlights integral sector area sweeps $A = 1/2 \int r^2 d\theta$ and visualizes the geometric backward-rendering anomaly when traversing negative radii.