Riemann Sum Explorer
Interactively approximate definite integrals using left, right, and midpoint Riemann sums. Adjust the number of rectangles to watch the approximation converge to the true area under the curve.
Derivative & Tangent Line Visualizer
Drag a point along any differentiable function to see the tangent line update in real time. Visualize how the slope of the tangent equals the derivative value, and explore where derivatives are zero or undefined.
Slope Field Explorer
Generate slope fields for any first-order ODE and trace solution curves through arbitrary initial conditions. Visualize how solutions behave near equilibria, and develop intuition for qualitative analysis.
Limits & Continuity
Explore five classic function types — removable holes, jump discontinuities, vertical asymptotes, continuous functions, and oscillating functions. Drag the approach point a and adjust the delta neighborhood to see left/right limits update in real time. Automatically identifies continuity.
Fundamental Theorem of Calculus
Visualize both parts of the FTC side by side: the integrand f(x) with shaded area and Riemann approximation, and the accumulation function F(x) = integral from a to x. Adjust bounds a and b, choose from five functions, and watch exact vs Riemann error update in real time.
Taylor & Maclaurin Series
Watch Taylor polynomial approximations converge to sin(x), cos(x), eˣ, ln(1+x), and 1/(1-x). Adjust the number of terms (1-12) and center point a. Individual terms shown as dashed colored lines; sum shown in purple. Max error and radius of convergence displayed live.