Unformatted text preview: f : D → R is continuous. * Note: This is book problem 1. 2. Prove that f : R → R given by f ( x ) = x 3 is not uniformly continuous. * Note: This is book problem 5. 3. Suppose that f : ( a, b ) → R is uniformly continuous. prove that f is bounded. ** Note: This is book problem 10. Section 3.5 1. De±ne f ( x ) = √ x for x ≥ 0. Verify the ǫ-δ criterion for continuity at x = 4. ** Note: This is part of book problem 2. There’s a hint in the book. 2. De±ne * f ( x ) = b x + 1 if x ≤ 3 4 2 if x > 3 4 Use the ǫ-δ criterion to show that f is not continuous at x = 3 4 . Note: This is book problem 4....
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This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08