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math 230 quiz 3 - x = √ t 1,y = t 2-3 t,z = cos πt(a...

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Math 230 Quiz #3 Fall 2010 Name Section Instructions: You may use your book and notes. You may not work with others. Take as much time as you need. The quiz is due in class on Monday. 1. Consider the curve C given by the following vector-valued function: ~ r ( t ) = D t - 1 , t, t E . Find all points of intersection of C with the ellipsoid defined by the equation 2 x 2 + y 2 + 2 z 2 = 10 . 1
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Math 230 Quiz #3 Fall 2010 2. Consider the space curve C given by the parametric equations:
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Unformatted text preview: x = √ t + 1 ,y = t 2-3 t,z = cos( πt ) (a) Write the parametric equations of the tangent line to C at the point (1 , , 1). (b) Find the unit tangent vector to C when t = 3. (c) Find the normal plane to the curve at the point (2 , ,-1). 2 Math 230 Quiz #3 Fall 2010 3. Calculate the curvature of the curve ~ r ( t ) = ± 2 3 t 3 ,t 2 ,t + 2 ² at the point ( 2 3 , 1 , 3). 3...
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