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Unformatted text preview: easy polar conversions, i.e. x 2 + y 2 , that cause cancelations in your function. Example 1 lim ( x,y ) → (0 , 0) cos ± x 2y 4 x 2 + y 2 ² Example 2 lim ( x,y ) → (0 , 0) xy p x 2 + y 2 5 Continuity Defn. Continuous f ( x, y ) is continuous at ( a, b ) if 1. 2. 3. Examples Find where the following functions are continuous. 1. f ( x, y ) = xy x + y 2. f ( x, y, z ) = √ xy + z 3. f ( x, y ) = 2 6 Do. 1. lim ( x,y,z ) → (1 , 3 ,2) x + 2 yz xyz 2. lim ( x,y ) → (0 , 0) x 2y x 2 + y 7...
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 Spring '03
 MECothren
 Calculus, Topology, Continuity, Multivariable Calculus, Limits, lim

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