Engineering Calculus Notes 418

Engineering Calculus Notes 418 - x 2 1 2 + y 2 2 2 + z 2 (1...

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406 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION x y z Figure 3.40: Vertical sections the “vertices”, or ends of the major and minor axes lie. These are the intersections of our surface with the two vertical coordinate planes (Figure 3.40 ). In Figure 3.41 we sketch the surface 4 x 2 + y 2 + 16 z 2 = 4 which can be expressed more informatively as
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Unformatted text preview: x 2 1 2 + y 2 2 2 + z 2 (1 / 2) 2 = 1; this is called an ellipsoid ; note that the three “axes” of our ±gure (along the coordinate axes) are precisely the square roots of the denominators of the second expression: 1 , 2 , 1 2 respectively. x y z Figure 3.41: Ellipsoid 4 x 2 + y 2 + 16 z 2 = 4...
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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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