Engineering Calculus Notes 413

Engineering Calculus Notes 413 - k =2 k =1 Figure 3.33...

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3.10. QUADRATIC CURVES AND SURFACES 401 x y z Figure 3.32: x 2 y + z = 0 intersects each horizontal plane z = k with k > 0 in an ellipse of the form x 2 + y 2 4 = k 4 ; it is immediate that the major axis is parallel to the y -axis, while the minor axis is half as long, and is parallel to the x -axis (Figure 3.33 ). k =4 k =3
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Unformatted text preview: k =2 k =1 Figure 3.33: Level sets: x 2 + y 2 4 = k 4 To see how these ellipses ±t together, we consider the intersection of the surface with the two vertical coordinate planes. The intersection with the xz-plane ( y = 0) has equation z = 4 x 2...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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