09hw4 - lim n →∞ Z 1 sin ± 2 x nπ 2 n x ² dx 9 Let f...

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Mathematics 241, Problem Set #4, due September 21, 2009 Write clear proofs that have good grammar and consist of complete sentences. 1. Royden, page 89, #3 2. Royden, page 89, #4 3. Royden, page 89, #5 4. Royden, page 89, #6 5. Royden, page 89, #7 6. Royden, page 93, #14 7. Royden, page 93, #15 8. Compute:
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Unformatted text preview: lim n →∞ Z 1 sin ± 2 x + nπ 2 n + x ² dx. 9. Let f be a bounded measurable function that vanishes outside a set of finite measure. For each y± R , define: F ( y ) = Z ∞ e-yx f ( x ) dx. Prove that F is a continuous function. F is called the Laplace Transform of f ....
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This note was uploaded on 11/18/2009 for the course MATH 241 taught by Professor Reed during the Spring '09 term at Duke.

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