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Engineering Calculus Notes 167

Engineering Calculus Notes 167 - Practice problems 1...

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2.2. PARAMETRIZED CURVES 155 which gives the distance from the yz -plane and the x -axis. The translation back is x = X y = 1 2 Y z = 1 2 Y. Then a circle of radius 1 centered at the origin but lying in the plane is given by the parametrization X = cos t Y = sin t and the translation of this to space coordinates is x = cos t y = 1 2 sin t z = 1 2 sin t or −→ p ( t ) = (cos t, 1 2 sin t, 1 2 sin t ) . This is sketched in Figure 2.24 . Exercises for § 2.2
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Unformatted text preview: Practice problems: 1. Parametrize each plane curve below, indicating an interval of parameter values over which the curve is traversed once: (a) The circle of radius 5 with center (2 , 3). (b) The ellipse centered at (1 , 2) with horizontal semimajor axis 3 and vertical semiminor axis 1. (c) The upper branch of the hyperbola y 2 − x 2 = 4....
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