Engineering Calculus Notes 422

Engineering Calculus Notes 422 - two vertical coordinate...

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410 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION intersects the horizontal plane z = k in the locus of the equation x 2 + y 2 = k 2 1; for | k | < 1 the right side is negative, so there is no intersection; for | k | > 1 we again get a circle centered on the z -axis, with radius k 2 1 (Figure 3.48 ). x y z Figure 3.48: Horizontal Sections To see how these ±t together, we intersect the surface with the
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Unformatted text preview: two vertical coordinate planes. The intersection with the xz-plane has equation x 2 = z 2 1 or z 2 x 2 = 1, which is a hyperbola opening vertically; the intersection with the yz-plane is essentially identical (Figure 3.49 ) x y z Figure 3.49: Vertical Sections...
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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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