Engineering Calculus Notes 166

Engineering Calculus Notes 166 - 1 which are distance √ 2...

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154 CHAPTER 2. CURVES and then substitution into the equation of the plane gives us z = sin t. Thus, this curve can be described by the function −→ p : R R 3 −→ p ( t ) = (cos t, sin t, sin t ) . It is shown in Figure 2.23 . Note that it is an ellipse , not a circle (for example, it intersects the x-axis in a line of length 2, but it intersects the yz -plane in the points (0 , ± 1 ,
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Unformatted text preview: 1), which are distance √ 2 apart). x y z Figure 2.23: Intersection of the Cylinder x 2 + y 2 = 1 and the Plane y + z = 0. How would we parametrize a circle in the plane y + z = 0, centered at the origin? One way is to set up a rectangular coordinate system (much like we did for conic sections) given by X = x Y = y √ 2...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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