SpecEnvoy
EN·中文

Calculus

Grade 12 calculus rests on one move: getting infinitely close to something. These demos let you watch that limit happen, so the ideas land as pictures, not just rules. Aimed at Grade 12 (Ontario MCV4U and equivalents).

Start here
Limits
What f(x) heads toward
The idea underneath everything: close in on a point from both sides and read where the function is going — even across a hole, a jump or a blow-up. A live table of values makes "arbitrarily close" concrete.
Open the demo →
Available now
Secant → Tangent
The derivative
Drag two points on a curve toward each other and watch the secant line become the tangent — and its slope become the derivative f ′(a). The single most important idea in the course, made visible.
Open the demo →
Available now
Riemann Sums
The integral
Slice the area under a curve into rectangles and crank up the number of slices — watch the sum settle on the exact integral. Left, right, midpoint and trapezoid rules, plus negative area.
Open the demo →

More on the way — see also Vectors & the Dot Product.