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Unformatted text preview: s compact. Does it follow that the set S is compact? Justify your answer. R R S f n : i 9. Is there a constant such that the function R c = + + = ) , ( ) , ( ) , ( ) , ( ) , ( 2 2 3 y x for c y x for y x y xy y x f is continuous at (0, 0)? Justify your answer. 10. Evaluate the following limits or prove that they do not exist (a) ) 1 , 1 ( ) , ( lim y x 4 3 4 y x y x (b) ) , ( ) , ( lim y x 2 2 2 2 2 ) ( ) cos( 1 y x y x + + (c) ) , , ( ) , , ( lim z y x 2 2 2 z y x xz yz xy + + + + Knowing: all the definitions, precise formulation of all the Theorems done on the lecture and the proofs of the few Theorems listed below is also part of the Assignment. 1.4, 1.13, 1.14, 1.22, 1.26....
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- Fall '09