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Unformatted text preview: ( x1) 4( y1) 4 x y z z = P 2 ( x, y ) FIGURE 3 FIGURE 4 Answer: P 2 ( x, y ) = 5x + y • The graph of P 2 is a plane. † Lecture notes to accompany Section 14.7 of Calculus by HughesHallett et al. 1 Math 10C. Lecture Examples. (11/11/08) Section 14.7, p. 2 Example 4 Figure 5 shows the graph of f ( x , y ) = y 21 12 y 4x , and Figure 6 shows its graph with the graph of its seconddegree Taylor polynomial z = P 2 ( x , y ) at x = , y = . Give a formula for P 2 ( x , y ) . x y z z = y 21 12 y 4x x y z z = P 2 ( x, y ) FIGURE 5 FIGURE 6 Answer: P 2 ( x, y ) = y 2x...
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 Spring '07
 Hohnhold
 Calculus, Derivative, Taylor Series

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