CalcLens early prototype

Interactive demonstrations for Calculus 1 — limits, derivatives and integrals — built the same way as StatLens: no build step, keyboard-first, readable on a phone, and aimed squarely at the places students actually get stuck.

Cards without a link are sketched, not built. URL parameters for the working tools are frozen — see the URL API.

Integrals

Accumulation Function Slide x and watch A(x) = ∫ₐˣ f build itself. The height of f is the slope of A — the Fundamental Theorem, on screen.
Riemann Sums Left, right, midpoint and trapezoid rectangles with an n slider and a live error table.
u-Substitution Watch the region transform when the variable changes — and see why du is not decoration.

Derivatives

Secant to Tangent Hold P still, slide Q in, and watch the difference quotient converge — with a table that approaches from either side. Works for any function, and strips down to a lecture figure. Derivative Builder Drag a point along f, drop each tangent slope onto a second axis, and watch f′ draw itself. Includes the secant-to-tangent limit.
Local Linearity Zoom Zoom until the curve looks straight — with |x| at the origin as the control case that never does.
Match the Triple Given three graphs, decide which is f, which is f′ and which is f″.
Related Rates An animated ladder, cone or shadow with every rate read out live as the picture moves.

Limits

Squeeze Theorem Three curves and a closing trap. Zoom in and watch the outer two pinch until g has nowhere to go — without ever evaluating g at the point.
Limit Explorer Table and graph together, approaching from both sides, with the one-sided values side by side.
Epsilon–Delta Game Someone picks ε; you find a δ that works. Repeat until the definition stops being frightening.
Continuity Classifier Removable, jump, or infinite — sort discontinuities by what the one-sided limits do.

Tools

Function Evaluator Type a function and the values you want it at. Closes in on a point from both sides for a limit table, and says undefined where the function has no value rather than hiding the row. Check My Answer Type a derivative or antiderivative and find out if it is right — by the same differentiate-and-compare method you should use on paper.

About this prototype

CalcLens has its own small computer algebra system — about 950 lines in js/expr.js — rather than a general library. Calculus 1 needs a narrow catalogue of functions, but it needs the answers printed the way the course prints them: ln x rather than log(x), x³⁄3 rather than 0.3333x³. Owning the printer is the point.

Student answers are checked by evaluating both sides at a spread of points, not by symbolic comparison. That never rejects a correct answer for being written in an unexpected form, and it hands back a specific counterexample when the answer is genuinely wrong.

Notes on the architecture, the supported syntax and what is still missing are in calclens/README.md. Page chrome, charts and maths rendering come from the shared kit/.