Polynomial End Behavior Analyzer
Visualize how the degree and leading coefficient of a polynomial determine its end behavior. Adjust coefficients interactively and observe limit notation for x→±∞ in real time.
Rational Function Asymptotes
Explore vertical, horizontal, and slant asymptotes of rational functions. Switch between preset functions or enter custom numerator/denominator coefficients to see asymptote detection in real time.
Unit Circle Navigator
Navigate the unit circle interactively. Drag or select angles to see exact sine, cosine, and tangent values. Visualize reference angles, quadrant signs, and the right triangle projection.
Exponential Growth vs Decay Comparison
Compare exponential growth and decay side by side. Adjust the initial value and base to see how doubling time, half-life, and growth rate change. Includes real-world presets like compound interest and radioactive decay.
Logarithmic Scale Visualizer
Explore how logarithmic scales compress vast data ranges. Switch between Richter earthquake magnitude, decibel sound levels, and pH acidity scales to see real-world log₁₀ applications.
Trig Identities Verifier
Verify trigonometric identities graphically. Select from Pythagorean, double-angle, cofunction, and reciprocal identities to see LHS and RHS overlaid on the same graph with a difference curve.
Polar Coordinate Plotter
Plot and explore polar curves interactively. Choose from circles, cardioids, rose curves, spirals, limaçons, lemniscates, and butterfly curves. Adjust parameters and watch animated tracing.
Compound Interest & Continuous Growth
Compare discrete and continuous compound interest. Adjust principal, rate, time, and compounding frequency to see how A = P(1+r/n)^(nt) approaches A = Pe^(rt). Includes the Rule of 72.
Polynomial Long Division & Remainder
Step-by-step polynomial long division solver. Enter dividend and divisor coefficients to see each division, multiplication, and subtraction step with quotient and remainder.
Sinusoidal Regression (Real Data)
Fit y = A sin(Bx + C) + D to periodic real-world data. Adjust amplitude, period, phase, and vertical shift with temperature, daylight, and tides presets.
Complex Zeros & Fundamental Theorem
Visualize all roots of a degree-4 polynomial on both the real graph and complex plane. See conjugate pairs, adjust real and complex roots dynamically.
2D Vector Component Decomposition
Interactive vector decomposition: adjust magnitude and angle to see Vx = |V|cos θ and Vy = |V|sin θ components on a grid with right-angle marker.
Conic Sections Explorer
Interactive conic sections explorer with adjustable semi-major/semi-minor axes. Visualizes foci (red), vertices (green), directrix (amber), and asymptotes. Shows standard form equation, eccentricity, and focal distance for Circle, Ellipse, Parabola, and Hyperbola.
Sequences & Series Explorer
Dual-panel sequences and series explorer. Top: bar chart of individual terms aₙ. Bottom: line chart of cumulative partial sums Sₙ with S∞ convergence line. Covers Arithmetic, Geometric (divergent and convergent |r|<1), and Harmonic sequences with adjustable parameters.