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Unformatted text preview: Find the value of f (ln 2) when f ( x ) = 2 e 2 x , f (0) = 5 . 1. f (ln 2) = 9 2. f (ln 2) = 8 correct 3. f (ln 2) = 11 4. f (ln 2) = 12 5. f (ln 2) = 10 Explanation: Since d dx e αx = αe αx , we see that f ( x ) = e 2 x + C where the arbitrary constant C is speci±ed by the condition f (0) = 5. For then f (0) = 5 = ⇒ 1 + C = 5 , in which case f ( x ) = e 2 x + 4 . On the other hand, e 2 x f f f x =ln 2 = e 2 ln 2 = e ln 4 = 4 . Consequently, f (ln 2) = 4 + 4 = 8 . keywords: antiderivative, exponential function, function value,...
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This note was uploaded on 02/14/2012 for the course MATH 408 K taught by Professor Clark,c.w./hoy,r.r during the Spring '08 term at University of Texas.
 Spring '08
 CLARK,C.W./HOY,R.R
 Antiderivatives, Derivative

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