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Home  Partial Differentiation Total Differentials and Tangent Planes The Tangent Plane |
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The Tangent Plane
DEFINITION The tangent plane of a smooth function z = f(x, y) at (a, b) is the plane with the equation z - f(a, b) = fx(a, b)(x - a)+ fy(a, b)(y - b). If we set x = a and y = b in this equation we get z = f(a, b). If we set x - a = dx and y - b = dy we get z - f(a, b) = dz. Therefore: The tangent plane touches the surface at (a, b). Δz = change in z on the surface. dz = change in z on the tangent plane. Figure 11.4.5 shows Δz and dz.
Figure 11.4.5
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Last Update: 2010-11-25