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Unformatted text preview: e x is C 1 and its derivative is e x . (g) Prove that e x is monotone from (∞ , ∞ ) to all of (0 , ∞ ) and so deFne an inverse function log( x ). (h) Using (f), prove that d dx log( x ) = 1 x . 1 2 HOMEWORK SET 7 DUE AT 1:00 PM ON MONDAY, NOVEMBER 14, 2005 (2) [20 points] Apostol, page 278, problems 3 and 9. Note : In these problems, T n ( f ( x )) denotes the Taylor approximation of order n about x = 0. (3) [10 points] Apostol, page 438, problems 5 and 10. (4) [20 points] Apostol, page 295, problems 1, 4, 8, and 11....
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This note was uploaded on 03/30/2010 for the course MA 1a taught by Professor Borodin,a during the Fall '08 term at Caltech.
 Fall '08
 Borodin,A
 Math

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