Calculus

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Vector tangent to a 3D surface path.

Illustration of a 3D surface with a path c(t) passing through the point (x0,y0,z0), showing the tangent vector v along the path and a parametric equation for the line on the surface.

This illustration depicts a tangent vector to a path c(t) on a 3D surface defined by S, z = k(x, y). The point of interest (x0, y0, z0) lies on both the surface and the path, with the tangent vector v indicating the direction of motion along the path at that point. The accompanying parametric equation for the line emphasizes the relationship between changes in x, y, and z along the curve.

This graphic is ideal for textbooks in calculus, engineering mathematics, and physics, providing a practical look at paths on 3D surfaces and directional derivatives.

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