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Unformatted text preview: denominator can be much more complicated than for one variable, if the discontinuity is essential. Exercises for 3.1 Practice problems: 1. or each function below, nd its limit as ( x,y ) (0 , 0): (a) sin( x 2 + y 2 ) x 2 + y 2 (b) x 2 r x 2 + y 2 (c) x 2 x 2 + y 2 (d) 2 x 2 y x 2 + y 2 (e) e x y (f) ( x + y ) 2 ( x y ) 2 xy (g) x 3 y 3 x 2 + y 2 (h) sin( xy ) y (i) e xy 1 y (j) cos( xy ) 1 x 2 y 2 (k) xy x 2 + y 2 + 2 (l) ( x y ) 2 x 2 + y 2 2. ind the limit of each function as ( x,y,z ) (0 , , 0): (a) 2 x 2 y cos z x 2 + y 2 (b) xyz x 2 + y 2 + z 2 Theory problems: 3. Prove Remark 3.1.2 . 4. Prove Proposition 3.1.4 ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Continuity, Limits

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