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Unformatted text preview: n ) . Now just observe that the right hand side is x a f . This line of reasoning is just what we used to prove Theorem 2 in the rst place. 5.25 For any vector a b c , dene the polynomial p ( x ) = a + bx + cx 2 . In turn, dene the number R 1 p ( x )d x . Putting the pieces together, we get a function f from IR 3 to IR we dene f a b c = Z 1 a + bx + cx 2 d x . (a) Show that f is a linear functional on IR 3 ; i.e., a linear transformation from IR 3 to IR . 21 /september/ 2005; 22:09 43...
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 Fall '08
 Gladue
 Calculus, Vectors

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