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Unformatted text preview: Math 13 Exam 2 Review Spring 2007 No calculators should be used in these problems. Simplify your answers as much as possible and box your answers. Write your solutions neatly, linearly, and in complete sentences. Show your work step by step. Model solutions will be posted on the Math 13 website at blackboard.tufts.edu on Thursday, March 8. The exam may contain other questions similar to homework problems. If you desire further practice, you will find some old exams and solutions from previous years on the Math 13 website. 1. Use the chain rule to find z/s when s = and t = 4, where z = e xy tan y, x = st, y = s t . 2. Let T ( x, y, z ) = x 2 + y 3 + z 4 . (a) Find the gradient vector vector T ( x, y, z ) at an arbitrary point ( x, y, z ). (b) Find a unit vector in the direction of which T ( x, y, z ) increases the fastest at the point ( 2 , 1 , 1). (c) What is the fastest rate of increase of T ( x, y, z ) at the point ( 2 , 1 , 1)?...
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- Fall '07