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**Unformatted text preview: **Lecture 7: Tangent Planes and Linear Approximations May 14, 2009 Lecture 7: Tangent Planes and Linear Approximations Objectives 1 Find the equation of a plane tangent to the graph of f ( x , y ). 2 Compute the linearization of a function f ( x , y ). 3 Calculate differentials of z = f ( x , y ). 4 Apply the concepts of linearization and differentials to estimation problems. Lecture 7: Tangent Planes and Linear Approximations Finding the tangent plane. In two dimensions, we constructed lines tangent to the graph of a function f ( x ) at a point x . Lecture 7: Tangent Planes and Linear Approximations Finding the tangent plane. In two dimensions, we constructed lines tangent to the graph of a function f ( x ) at a point x . y- f ( x o ) = f ( x )( x- x ) Lecture 7: Tangent Planes and Linear Approximations Finding the tangent plane. In two dimensions, we constructed lines tangent to the graph of a function f ( x ) at a point x . y- f ( x o ) = f ( x )( x- x ) In three dimensions, the graph of f ( x , y ) is a surface, and our goal is to find the plane that is tangent to the surface at a point ( x , y ). Lecture 7: Tangent Planes and Linear Approximations Finding the tangent plane. In two dimensions, we constructed lines tangent to the graph of a function f ( x ) at a point x ....

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