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# mid1n - 2 sin x 2 dx by using the ±rst four non-zero terms...

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Math 126 C - Winter 2006 Mid-Term Exam Number One January 31, 2006 Name: Section: 1 10 2 10 3 10 4 10 5 10 6 10 7 10 Total 70 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. Find the 2nd-degree Taylor polynomial, T 2 ( x ) for the function f ( x ) = ln(ln x ) based at x = e . 2. Approximate the integral integraldisplay

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Unformatted text preview: 2 sin( x 2 ) dx by using the ±rst four non-zero terms of a Taylor series. Given a decimal approximation of your result. 3. Write out the frst Four terms oF the Taylor series For the Function f ( x ) = 1 1 + 5 x + 1 3 + x 4. ±ind the angle between the vectors va = <-3 , 4 , 1 > and v b = < 3 , 1 , 1 > . Give a decimal value For the angle. 5. Suppose the vector < x, 3 , 2 > is orthogonal to the vector < 2 , 3 , x > . Find x . 6. Find the equation of the plane through the three points (-3 , 4 , 0) , (1 , 7 ,-3) and (2 ,-5 , 3) . 7. Find the equation of the plane containing the line of intersection of the two planes x + y-z = 3 and 2 x-3 y + 4 z = 5 and the point (-2 , 7 , 3) ....
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