Differentiable Surface Zooming Demo
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This example demonstrates the local zooming effect on differentiable surfaces, visually showing the smoothness of the surface in various regions. Key math concepts include differentiability, local linear approximation, and limit theory. The construction uses the GeoGebra function object 'f' to define the surface, with dynamic zooming to reveal surface details. Suitable for high school and above students studying calculus, multivariable functions, and spatial geometry, helping to understand the geometric meaning of limits and derivatives.
GeoGebra Commands & Parameters
f(x, y) = (x^(2) * y / sqrt(x^(2) + y^(2)))