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mid2w - t = 1 2 Does the curve defned by the polar equation...

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Math 126 C - Spring 2007 Mid-Term Exam Number Two May 10, 2007 Name: Section: 1 10 2 10 3 10 4 10 5 10 Total 50 Complete all questions. You may use a scientific, non-graphing calculator during this examination. Other elec- tronic devices are not allowed, and should be turned off for the duration of the exam. If you use a trial-and-error or guess-and-check method, or read a numerical solution from a graph on your calculator, when an algebraic method is available, you will not receive full credit. You may use one hand-written 8.5 by 11 inch page of notes. Show all work for full credit. You have 50 minutes to complete the exam. .
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1. Consider the curve defined by the vector equation −→ r ( t ) = ( 4 t, 5 t 3 , 2 t 2 ) (a) Find the unit tangent vector −→ T ( t ) at the point where t = 1 . (b) Find the parametric equations of the tangent line the curve at the point where
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Unformatted text preview: t = 1 . 2. Does the curve defned by the polar equation r = sec + tan intersect the vertical line x = 2 ? Explain. 3. Suppose a particle is moving in 3-dimensional space so that its position vector is r ( t ) = a t, t 2 , 1 t A . (a) Find the tangential component of the particles acceleration vector at time t = 1 . (b) Find all values of t at which the particles velocity vector is orthogonal to the parti-cles acceleration vector. 4. Consider the curve in the xy-plane defned by the position vector Function r ( t ) = a t 2 3 t, t 2 + 2 t A ind the t-value oF the point oF maximum curvature on this curve. 5. Let f ( x, y ) = xe y ln( x + y ) . (a) Sketch the domain of f . (b) Find f xy ( x, y ) ....
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