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Unformatted text preview: Problem 4. A not uncommon calculus mistake is to believe that the product rule for derivatives says that ( fg ) = f g . If f ( x ) = e x 2 determine, with proof, whether there exists an open interval ( a,b ) and a nonzero function g dened on ( a,b ) such that this wrong product rule is true for x in ( a,b ). [Putnam Exam, 1988, A-2]...
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- Fall '10