advcalc1sf - Advanced Calculus I, Dr. Block, Sample Final...

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Advanced Calculus I, Dr. Block, Sample Final Exam PART ONE: COMPLETE THE DEFINITIONS (4 definitions, 3 points each, 12 total points) 1. Suppose that D R , and f : D R . Suppose that a D and a is an accumulation point of D. We say that f is differentiable at a if and only if 2. Suppose that D R , and f : D R . Let c D. We say that f has a relative maximum at c if and only if 3. Suppose that D R , and f : D R . We say that f satisfies the intermediate value property on D if and only if 4. Suppose that D R , and f : D R . We say that f is a Lipschitz function if and only if PART TWO: PROOFS OF THEOREMS (2 proofs, 8 points each, 16 total points) 5. Prove the following: Suppose that D R , and f : D R . Suppose that a D and a is an accumulation point of D. If f is differentiable at a, then f is continuous at a. 6. State and Prove the Mean Value Thereom.
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PART THREE: PROBLEMS (3 problems, 8 points each, 24 total points). 7. Locate and classify all the points of discontinuity of f. Justify your answer. f : [0
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This note was uploaded on 01/03/2012 for the course MAA 4102 taught by Professor Dr.vince during the Fall '09 term at University of Florida.

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advcalc1sf - Advanced Calculus I, Dr. Block, Sample Final...

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