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Unformatted text preview: an extreme point. Exercise 4 : Show that if { x n } n =1 is a sequence of real numbers that converges to the point x o R then  x n   x o  as n . Otherwise said, the absolute value function is continuous. Exercise 5 : Show that the function f ( x ) = x 2 is continuous at any real x o by showing that if { x n } n =1 is any sequence with lim n x n = x o then lim n f ( x n ) = f ( x o ). (HINT: x 2y 2 = ( x + y )( xy ) and, since x n x o , then for n suciently large,  x n + x o  is bounded by 3  x o  .)...
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This note was uploaded on 02/20/2011 for the course MATH 530 taught by Professor Luke,d during the Fall '08 term at University of Delaware.
 Fall '08
 Luke,D
 Math

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