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mid1o - error | f x − T 2 x | on the interval(0 75 1 25 2...

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Math 126 C, D - Spring 2006 Mid-Term Exam Number One April 20, 2006 Name: Section: 1 10 2 10 3 10 4 10 5 10 6 10 Total 60 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. Let f ( x ) = 3 7 x 4 x 2 + 6 x 3 . (a) Find the 2nd-degree Taylor polynomial T 2 ( x ) for f ( x ) based at b = 1 . (b) Use the Quadratic Approximation Error Estimate to give an upper bound on the
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Unformatted text preview: error | f ( x ) − T 2 ( x ) | on the interval (0 . 75 , 1 . 25) . 2. Give the coefFcient on x 11 in the Taylor series for f ( x ) = x 3 e x 2 based at b = 0 . 3. Find a vector that is orthogonal to the vector a 11 , 3 , − 5 A and has length 7 . 4. Find the parametric equations for the line that is the intersection of the plane x + y + 2 z = 1 and the plane 3 x − y + 4 z = 1 . 5. The set of points that are twice as far from the origin as they are from the point (5 , 5 , 5) is a sphere. Find its center and radius. 6. Find the equation of the plane that passes through the point (3 , − 1 , 2) and contains the line x = 5 − t, y = 3 + 3 t, z = 8 + 2 t....
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