15_R_11 - F x y = x i-y j p x 2 y 2 which is continuous...

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11. Since the field lines of F are xy = C , and so satisfy y dx + x dy = 0 , or dx x = - dy y , thus F = λ( x , y )( x i - y j ) . Since | F ( x , y ) | = 1 if ( x , y ) 6= ( 0 , 0 ) , λ( x , y ) = ± 1 / p x 2 + y 2 , and F ( x , y ) = ± x i - y j p x 2 + y 2 . Since F ( 1 , 1 ) = ( i - j )/ 2, we need the plus sign. Thus
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Unformatted text preview: F ( x , y ) = x i-y j p x 2 + y 2 , which is continuous everywhere except at ( , ) ....
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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