Advanced Graphing Calculator

Graph mathematical functions, compute derivatives and integrals, find critical points, and explore parametric and polar equations with an interactive visual display. Supports multiple functions, calculus analysis, and advanced coordinate systems.

This calculator switches between five entirely independent modes based on Graphing Mode (lines 34-263): Standard Graphing plots up to four functions of x at once; Calculus Analysis takes a single function and derives its symbolic derivative, a numerical definite integral via Simpson's rule (1,000 steps, lib/math-expression.ts), roots by bisection, and critical points by finding where the derivative crosses zero and classifying each with a second-derivative test; Parametric and Polar modes trace curves defined by a parameter t or angle θ; and Limits mode estimates a two-sided limit by evaluating the function at five shrinking distances (0.1 down to 0.00001) from the approach point and checking whether the left- and right-hand values agree within 0.0001. In the default mode (Standard Graphing, with only f₁(x) = sin(x) filled in), the internal count of how many functions are active is completely unaffected by every numeric input on the page — X Min, X Max, t max, and θ max all leave it unchanged, because that count is just the number of the four function fields that are non-blank and successfully parsed — a field left blank, or one that fails to parse, is skipped before it reaches the count (lines 38-44, 64); it never reads a numeric input at all, and t max and θ max in particular belong to modes (Parametric and Polar) the calculator isn't even running while in Standard Graphing mode. In Standard Graphing and Calculus Analysis modes, a point where evaluation throws or returns a non-finite value (for example, dividing by zero) is not silently dropped — generatePoints (lib/math-expression.ts:101-131) explicitly records it as `{x, y: null}`, a marked discontinuity the chart can render as a gap rather than an invented value. Parametric and Polar modes handle the same situation differently: generateParametricPoints and generatePolarPoints (lib/math-expression.ts:139-210) both skip a failing point without recording anything at all, so a discontinuity in those two modes leaves no gap marker — the curve simply has one fewer point there. Critical-point classification treats a second derivative between −0.001 and 0.001 as an inflection point rather than attempting an exact symbolic test. This calculator does not distinguish why a point failed to evaluate — a genuine vertical asymptote (like x = 0 in 1/x) and a single removable hole in an otherwise continuous curve both just produce the same null-marked gap or missing point, with no separate classification of which kind of discontinuity it is.