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Unformatted text preview: x 3 = y1 = 2z and the point P (1 , 2 , 3) 2. Find parametric equations of the tangent line to the curve. r ( t ) = h 1 + 2 √ t,t 3t,t 3 + t i at the point P (3 , , 2). Find its curvature at this point as well. [Easier without computing T ( t )] 3. Write parametric equations for the curve of intersection of the surfaces y = x 2 and x 2 + 4 y 2 + 4 z 2 = 16. 4. Sketch the curves: a) r ( t ) = h t, cos t, 3 sin t i b) r ( t ) = h 2 , cos t, 3 sin t i c) r ( t ) = h t 2 ,t, 4 i d) r ( t ) = h 5 sin 2 t, 5 cos 2 t,1 i e) Find the curvature κ ( t ) for c). f) Find the curvature κ ( t ) for d). 5. Show that the circular helix r ( t ) = h a cos t,a sin t,bt i , where a and b are positive constants, has constant curvature....
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This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.
 Spring '08
 Keeran
 Calculus, Geometry, Arc Length

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