Practice: the second-step error
Suppose we start at (a, b) and use the tangent plane at (a, b) to approximate f(a + Δx, b + Δy). We move in two coordinate steps:
- (a, b) → (a + Δx, b)
- (a + Δx, b) → (a + Δx, b + Δy)
Define error as actual height change − estimated height change.