15.2Ex18-23

15.2Ex18-23 - S E C T I O N 15.2 Limits and Continuity in Several Variables(ET Section 14.2 629 18 x y,0 sin y lim sin x We examine the limits as(x

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SECTION 15.2 Limits and Continuity in Several Variables (ET Section 14.2) 629 18. lim ( x , y ) ( π , 0 ) sin x sin y SOLUTION We examine the limits as ( x , y ) approaches ( , 0 ) along the line x = and along the line y = x : lim ( x , y ) ( , 0 ) along x = sin x sin y = lim y 0 sin sin y = lim y 0 0 sin y = lim y 0 0 = 0 lim ( x , y ) ( , 0 ) along y = x sin x sin y = lim x sin x sin ( x ) = lim x sin x sin x = lim x ( 1 ) =− 1 The two limits are different, therefore the given limit does not exist. In Exercises 19–22, assume that lim ( x , y ) ( 2 , 5 ) f ( x , y ) = 3 , lim ( x , y ) ( 2 , 5 ) g ( x , y ) = 7 19. lim ( x , y ) ( 2 , 5 ) ( f ( x , y ) + 4 g ( x , y ) ) SOLUTION Using the Sum Law and the Constant Multiples Law we get lim ( x , y ) ( 2 , 5 ) ( f ( x , y ) + 4 g ( x , y )) = lim ( x , y ) ( 2 , 5 ) f ( x , y ) + 4 lim ( x , y ) ( 2 , 5 ) g ( x , y ) = 3 + 4 · 7 = 31
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This note was uploaded on 02/13/2010 for the course MATH MATH 32A taught by Professor Park during the Fall '09 term at UCLA.

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