surface example
3D Radial Decay Surface Graph
A smooth mound that decays toward zero.
z = 1 / (1 + x^2 + y^2)Teacher prompt
What value does z approach far away?
It approaches 0 as the denominator grows.
min z 0.00max z 0.0056 samples
What this graph represents
Distance increases the denominator, so the height falls off.
Where it appears in calculus
Use it for limits at infinity.
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Open embed pageRelated graphs
Open another surface page and compare shape, slices, and contour behavior.
Saddle Surface
z = x^2 - y^2A saddle surface curves up in one direction and down in the perpendicular direction.
Gaussian Surface
z = exp(-(x^2 + y^2))A smooth bell-shaped surface centered at the origin.
Elliptic Paraboloid
z = x^2 + y^2A bowl-shaped surface that opens upward.
Inverted Paraboloid
z = 12 - x^2 - y^2A dome-shaped surface with a highest point at the center.