202e104(Calc3) - Vector Calculus Exam I 10-11 AM Wednesday...

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Unformatted text preview: Vector Calculus Exam I 10-11 AM Wednesday March 3, 2004 in Olin 305, if you are registered in an even—numbered section, and in Bloomberg 272 (our usual lecture room) if you are registered in an odd— numbered section. [What section you actually attend is irrelevant] What is YOUR NAME?: What is YOUR SECTION NUMBER?: Extra Credit: Your TA’s FULL NAME: Even More Extra Credit: Your TA’S ASTROLOGICAL SIGN: General instructions: There are four problems, equally weighted. Please show any work for which you hope to get credit, because a correct answer is worth zero (0) points: it is part of the problem to give a reasonably lucid account of the reasoning behind your answer. No books or notes are allowed. Calculators are permitted, but no credit will be given for answers stated in terms of decimal numbers. May the Force be with you! 1 Calculate the length of the curve c : R ——> R3 defined by the function C(t) = (t sint + cost,tcost — sin t, 2) as t varies between t = 0 and t = 2. 2 The curves a(t) : (t,t2,t3) and b(u) = (sin2u,ucosu, u) intersect at the point (0, 0, 0). Find the cosine of the angle between the tangent lines to these curves at this intersection point. 3 Calculate the derivative of the function GU?) = 9($(t)ay(t)12(t)) defined by the path t I—-> (33,31, 2) = (sint,cost, et) and the function 9(957317 Z) =10g($2 + 292 + Z2) first directly, and then by using the chain rule. 4 Find the points on the surface S : {(37,972) I Z : fcray) : 3.’L‘y—£L‘3 ’y3} where the tangent plane is parallel to the plane 3x+3y+z=1. [Hintz you might try a: = i1 ...] ...
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