Sec12.6 - Sec. 12.6 Tangent Planes and Differentials In...

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Sec. 12.6 Tangent Planes and Differentials In single variable calculus, at a point on a differentiable function, the tangent line to the function at that point and the function are essentially the same. So it is with a point on a two-variable differentiable function and its tangent plane at that point. Thus if we can find the tangent plane at a point to a surface we can use it to estimate the value of the surface near that point. The gradient at a point on a surface is orthogonal to the tangent plane at that point on the surface. So using the equation of a plane:  0 0 nrr   we come up with 00 0 ,, 0 fx x y y z z     for the tangent plane.(sec12.5) (Implicit) The tangent plane to the level surface (, ,) 0 Fxyz at point 000 (, ,) Px y z is the plane that passes through P and has the normal vector F (x 0 ,y 0 ,z 0 ). So the equation of the tangent plane is   0 0 0 (,,) 0 xy z Fxyz x x Fxyz y y Fxyz z z   .
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This note was uploaded on 02/11/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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Sec12.6 - Sec. 12.6 Tangent Planes and Differentials In...

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