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Unformatted text preview: ( a, b ). ii) Suppose functions f, g : ( a, b ) R are continuous, and f ( r ) = g ( r ) for each rational number r in ( a, b ). Show that f ( x ) = g ( x ) for each x ( a, b ). 4. i) If we replace the closed interval [ a, b ] in theorem 18.1 by the open interval ( a, b ) the proof doesnt work. Explain why. ii) Show that the function in the question 1 has neither the maximum value or the minimum value on (1 , 2). 1...
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 Fall '07
 Fukuda

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