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Unformatted text preview: By the mean value theorem, there exists, for each , between + and such that ( + ) ( ) = ( x ) where x = ( 1 , 2 ,... , , , +1 + +1 ,... , + ). Therefore ( x + x ) ( x ) = =1 ( x ) Define the linear functional ( x ) = =1 ( x ) Then ( x + x ) ( x ) ( x ) = =1 ( ( x ) ( x ) ) and ( x + x ) ( x ) ( x ) =1 ( ( x ) ( x ) so that lim x ( x + x ) ( x ) ( x ) x =1 (...
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- Fall '10