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Unformatted text preview: In each case below, decide whether it is possible for a function f to be 5. continuous and unbounded on [0 , 1); 6. continuous and unbounded on [0 , 1]; 7. continuous on [0 , 1] with the range { f ( x ) : x ∈ [0 , 1] } = (0 , 1); 8. continuous on (0 , 1) with the range { f ( x ) : x ∈ (0 , 1) } = [0 , 1]; 9. continuous on (0 , 1) with the range { f ( x ) : x ∈ (0 , 1) } = [0 , 1] ∪ [3 , 4]. In each case justify your answer by giving an example or by quoting a theorem that shows that no example can exist. 1...
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This document was uploaded on 01/31/2011.
 Spring '09

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