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Fall 06 Exam 2 - Engineering Mathematics(E35 317 Exam 2...

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Engineering Mathematics (E35 317) Exam 2 October 18, 2006 This exam contains six free-response problems worth 27 points altogether, four short-answer problems worth one point each, and nine true-false problems worth one point each, for an exam total of 40 points. Part I. Free Response In each problem in this section, follow directions carefully, and needed to show all the steps arrive at the correct answer. The point value for each problem is shown to its left. (4) 1. Find an equation of the plane containing the points , , and E œ Ð$ß "ß "Ñ F œ Ð#ß !ß %Ñ G œ Ð"ß #ß "Ñ . (3) 2. Find parametric equations for the circle given by , . B  D  %D œ "# C œ " # #
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(5) 3. Consider the curve traced out by the vector function r . p Ð>Ñ œ Ò# #>ß #  #>ß > Ó cos sin # Find parametric equations or a vector equation for the tangent line to this curve at the point where . > œ 1 # (5) 4. Consider the scalar function 0ÐBß Cß DÑ œ C / $ BD (a) Find at the point . f0 Ð$ß #ß !Ñ (b) Find the directional derivative of at the point in the direction of the 0 Ð$ß #ß !Ñ vector a p œ Ò'ß $ß #ÓÞ
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