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Unformatted text preview: if x > 2 . 3 Exercise 3 ( 20 points ) At what points is the following function continuous? f ( x ) = ± 2 x if x ∈ N x 2 if x 6∈ N 4 Exercise 4 ( 25 points ) Show that there is a real number c ∈ (1 , 10 √ 2 ) such that f ( c ) = 0 . Here, f ( x ) = 1 ( x1) 2 + 1 x10 √ 2 . 5 Exercise 5 ( 20 points ) Find the least upper bound and the greatest lower bound for S = { . 9 , . 99 , . 999 , . 9999 , · · ·} 6...
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 Fall '08
 N/A
 Math, Calculus, Order theory, School of Mathematics, Prof. W. Gangbo

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