rev2_fall11_2313

# rev2_fall11_2313 - x 3 = y-1 = 2-z and the point P (1 , 2 ,...

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MAC 2313 Review Exam 2 09/19/2011 To know list: Find equation of a plane Distance between a point and a plane Find traces of quadratic surfaces Identify equations of quadratic surfaces. Rough sketch of quadratic surfaces. Vector functions, domain, limits, etc. Sketch of basic vector functions (space curves) Write vector function for described space curves. Properties of derivatives/integrals of r ( t ) Find the tangent line to a curve at given point Arc Length vs Arc Length function Arc Length reparametrization Curvature (its 3 deﬁnitions) Unit Tangent, Normal and Binormal vectors. Arc Length reparametrization Normal plane and Osculating plane Osculating circle. ***Knowledge of lines is still necessary!!*** 1. Find the equation of a plane containing the line
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Unformatted text preview: x 3 = y-1 = 2-z 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 3-t,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.

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