Calculus

• Taylor and Maclaurin polynomials – approximating functions Mathematics · Calculus Choose a function (sin x, cos x, eˣ, ln(1 + x), 1/(1 − x), arctan x), a centre a and a degree n, and watch the... Ages 16–17
• Implicit differentiation – tangents to curves F(x, y) = 0 Mathematics · Calculus Pick or type a curve F(x, y) = 0 (circle, ellipse, x² + xy + y² = k, hyperbola, folium of Descartes, a cubic curve... Ages 16–17
• Area between two curves Mathematics · Calculus Pick a pair of curves and watch the plane region between them get shaded. The simulation splits the region into thin... Ages 17–18
• Motion on a line with calculus – position, velocity, acceleration and distance Mathematics · Calculus Choose a position s(t), velocity v(t) or acceleration a(t) function (polynomial, trigonometric or exponential,... Ages 17–18
• Parametric curves – velocity, dy/dx and arc length Mathematics · Calculus Trace curves given by x(t) and y(t): a line, a circle, an ellipse, a projectile with g = 9.81 m/s², Lissajous... Ages 16–17
• Calculus grapher – f, f′, f″ and the antiderivative Mathematics · Calculus Drag to reshape the graph of f(x) with the hill, triangle, parabola, sine, freehand, shift and tilt tools, and watch... Ages 17–18
• Parabola and the tangent line at a moving point Mathematics · Calculus The graph of y = ax² + bx + c has a point M that moves along the parabola. Drag M with the mouse or a finger; the... Ages 16–17
• 3D Volumes of revolution – discs, washers, shells and cross-sections Mathematics · Calculus Rotate the region between y = f(x) and y = g(x) about the x-axis, the y-axis or a line y = k or x = k to build a 3D... Ages 17–18
• Integrals as a limit of rectangle areas Mathematics · Calculus The area of the curved region below the curve y = f(x) on [a, b] is approximated by n rectangles (left, right,... Ages 17–18
• Numerical root finding – change of sign, bisection, iteration and Newton–Raphson Mathematics · Calculus Choose a function f and see a table of values and signs on an interval, zoom in step by step to trap a root, and... Ages 16–17
• Related rates – sliding ladder, filling cone, ripple, balloon and shadow Mathematics · Calculus Five animated scenarios: a ladder sliding down a wall, water pouring into a conical tank, a circular ripple on a... Ages 16–17
• Real-world optimization with derivatives Mathematics · Calculus Pick a real-world problem – designing a can that uses the least material, folding an open-top box with the largest... Ages 17–18
• Differential equations – slope fields, particular solutions and Euler's method Mathematics · Calculus Choose dy/dx = f(x, y) (exponential growth or decay, y′ = ay + b, logistic growth, Newton's law of cooling, x + y,... Ages 17–18
• Secant to tangent – the derivative as a limit Mathematics · Calculus Drag two points P and Q on a curve to read the average rate of change (f(a + h) − f(a))/h, then shrink h and watch... Ages 16–17

No simulation matches your search.