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Unformatted text preview: Let f : [ a, b ] R be a continuous function. If f ( x ) > 0 for all x [ a, b ], then there exists a number c > 0 such that f ( x ) c for all x [ a, b ]. (Hint: Use Theorem 18.1.) Problem 5: Let f : R R be a continuous function for which f ( x ) Q for all x R . Prove that f must be a constant function. (Hint: Proof by contradiction.) Problem 6: Using Theorem 19.2, explain why the function f ( x ) = x 17 sin x-e x cos 3 x is uniformly continuous on [0 , ]....
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This note was uploaded on 03/18/2012 for the course MATH 67 taught by Professor Schilling during the Fall '07 term at UC Davis.
- Fall '07