Engineering Calculus Notes 296

Engineering Calculus Notes 296 - discussion above could...

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284 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION which can be obtained from the parametrization of the full tangent plane by fixing s = 0. (See Figure 3.12 .) -1 0 1 2 -1 0 1 2 −→ v x Figure 3.12: Slicing graph of x 2 3 y 2 2 at y = 1 2 The combined picture, together with the normal vector and tangent plane, is given in Figure 3.13 . The alert reader (this means you !) will have noticed that the whole
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Unformatted text preview: discussion above could have been applied to the graph of any di²erentiable function of two variables. We summarize it below. Remark 3.5.2. If the function f ( x,y ) is diFerentiable at −→ x = ( x ,y ) , then the plane tangent to the graph z = f ( x,y ) at x = x y = y ,...
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