1. Limits — ε/δ
$\lim_{x\to a} f(x) = L$. Drag ε. The required δ shrinks with it.
2. Tangent line
Drag the point. The line's slope is $f'(x_0)$ — the limit of secant slopes as $h\to 0$.
3. Optimization
Critical points: $f'(x)=0$. Use $f''$ to classify them. Slide the parameter to see how the landscape changes.
4. Riemann sums
$\int_a^b f(x)\,dx \approx \sum f(x_i^*)\,\Delta x$. Pick a method; slide $n$.
5. Area between two curves
$\int_a^b |f(x)-g(x)|\,dx$. Interval auto-clips to where curves are defined.
6. Taylor series
$f(x) \approx \sum_{k=0}^{N} \frac{f^{(k)}(a)}{k!}(x-a)^k$. Shaded band: radius of convergence.
7. Partial derivatives
Slice $z=f(x,y)$ along $y=y_0$ (red) and $x=x_0$ (teal). The slopes of the slices are $f_x$ and $f_y$.
8. Vector field
Arrow length is rescaled; colour is true magnitude.
9. Gradient + contour lines
$\nabla f$ points up the steepest slope — perpendicular to level sets.
10. 3D surface
Drag to rotate. Yellow dots: extrema. Orange: saddle.