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by: Adam Crona


Adam Crona
GPA 3.73

Karl Rubin

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About this Document

Karl Rubin
Class Notes
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This 1 page Class Notes was uploaded by Adam Crona on Saturday September 12, 2015. The Class Notes belongs to Math 194 at University of California - Irvine taught by Karl Rubin in Fall. Since its upload, it has received 9 views. For similar materials see /class/201861/math-194-university-of-california-irvine in Mathematics (M) at University of California - Irvine.

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Popular in Mathematics (M)




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Date Created: 09/12/15
Math 194 For discussion Tuesday Nov 18 2008 You are strongly urged to write up and hand in a careful and complete solution to at least one of these problems 1 F 9 7 U 03 Evaluate n 1 lim naoo kg 1 k2 n2 Larson 685 Let f 2Z2 1 sink with a E R n 2 1 Prove that if f S sinx for every s then Putnam 1967 Let f be a continuous function on 0 1 such that f0 f1 0 and 2ffy 3f2m3y for all my 6 01 Prove that f 0 for all z 6 01 Vietnamese Mathematical Olympiad 1999 Suppose f R a R is a continuous function such that 7 2 x 7y for every my 6 R Show that the range of f is R ie for every 0 E R there is an x such that fx c De Souza amp Silva Berkeley Problems in Mathematics Suppose that f R a R is a continuous function and de ne gltzgt we NW 0 Prove that if g is a nonincreasing function then fx 0 for every x Romanian Olympiad 1978 Let f 01 a R be a function with a continuous derivative such that f0 0 and 0 lt f S 1 for every x Show that 1 f96dz2 2 1f963dx Putnam 1973


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