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plugin-Math255-Pset9

# plugin-Math255-Pset9 - x-y plane bounded by the lines y =...

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Winter 2010 Math 255 Problem Set 9 Due on Mar 16 Section 16.1: 2,6,9. Section 16.2: 14,24,34. Section 16.3:14,20,42,50,52. Section 16.4:12,22,26,32,34,36. Challenge problems: 1. Let f ( x, y ) = xy ( x 2 - y 2 ) ( x 2 + y 2 ) 3 for ( x, y ) 6 = (0 , 0) and f (0 , 0) = 0. Show that Z 1 0 Z 2 0 f ( x, y ) dxdy 6 = Z 2 0 Z 1 0 f ( x, y ) dydx Why Fubini’s theorem does not hold? 2. Let D 1 be the region in the first quadrant of the x - y plane bounded by the lines y = x , y = x - 1 and D 2 be the region in the first quadrant of the

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Unformatted text preview: x-y plane bounded by the lines y = x-1 and y = x-2. Deﬁne the function f ( x,y ) by f ( x,y ) = 1 if ( x,y ) in D 1-1 if ( x,y ) in D 2 otherwise Show that Z ∞ Z ∞ f ( x,y ) dxdy 6 = Z ∞ Z ∞ f ( x,y ) dydx 1 Winter 2010 Math 255 Why Fubini’s theorem does not hold? 2...
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