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Unformatted text preview: probably encounter in higher math courses. Tangent Planes of Level Surfaces When a surface is dened by an equation in x , y and z , it is being presented as a level surface of a function f ( x,y,z ). Theorem 3.5.3 tells us that in theory, we can express the locus of such an equation near a regular point of f as the graph of a function expressing one of the variables in terms of the other two. rom this, we can in principle nd the tangent plane to the level surface at this point. However, this can be done directly from the dening equation, using the gradient or linearization of f . Suppose P ( x ,y ,z ) is a regular point of f , and suppose p ( t ) is a diFerentiable curve in the level surface L ( f,c ) through P (so c = f ( P )),...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08