Math252Sols5F08

Math252Sols5F08 - QUIZ 5(CHAPTER 18 SOLUTIONS MATH 252 FALL...

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QUIZ 5 (CHAPTER 18) SOLUTIONS MATH 252 – FALL 2008 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% Show all work, simplify as appropriate, and use “good form and procedure” (as in class). Box in your final answers! No notes or books allowed. A scientific calculator is allowed. 1) Matching. (9 points total) Fill in each blank below with a true property describing the vector field F . (Assume that we are only evaluating F on its domain.) A. The vectors in the field all have the same direction. B. The non- 0 vectors in the field all point away from the origin. C. The vectors in the field are all unit vectors. I. F x , y () = x i + y j . It is true that __B __ . If a point a , b is the initial point for a , b , the position vector to the point, then that vector will point away from the origin. II. F x , y = 2 i + 3 j . It is true that __A __ . F is a constant vector field. III. F x , y = 1 x 2 + y 2 ± x i ± y j . It is true that __C __ . ± x i ± y j = ± x 2 + ± y 2 = x 2 + y 2 Thus, F x , y = ± x i ± y j ± x i ± y j . This represents a normalization process.
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2) Let F x , y , z () = x 2 e 2 z , cos 3 y , xy 2 z 3 ± x . (20 points total) a) Find div F . div F = ± F = ² ² x , ² ² y , ² ² z x 2 e 2 z , cos 3 y , xy 2 z 3 ³ x = ² ² x x 2 e 2 z + ² ² y cos 3 y + ² ² z xy 2 z 3 ³ x = 2 x e 2 z ´ µ · + ³ 3sin 3 y ´ µ · + xy 2 3 z 2 ´ µ · = 2 xe 2 z ³ 3sin 3 y + 3 xy 2 z 2 b) Find curl F . curl F = ±² F = ij k ³ ³ x ³ ³ y ³ ³ z x 2 e 2 z cos 3 y xy 2 z 3 ´ x = ³ ³ y xy 2 z 3 ´ x ´ ³ ³ z cos 3 y µ · ¸ ¹ º i ´ ³ ³ x xy 2 z 3 ´ x ´ ³ ³ z x 2 e 2 z µ · ¸ ¹ º j + ³ ³ x cos 3 y ´ ³ ³ y x 2 e 2 z µ ·
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This note was uploaded on 09/08/2011 for the course MATH 252 taught by Professor Staff during the Spring '11 term at Mesa CC.

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Math252Sols5F08 - QUIZ 5(CHAPTER 18 SOLUTIONS MATH 252 FALL...

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