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Unformatted text preview: X n = 1 (-2 ) n n ( x + 3 ) n 3. (a) Write f ( x ) = x ( 1-x ) 2 as a power series. (b) Substitute x = 1 2 in your answer in part (a) and thus, or otherwise, nd X n = 1 n 2 n . 4. Consider the function f ( x ) = cos ( x ) . (a) Find the Mclaurin series of f ( x ) . (b) If f ( x ) is approximated by 1-x 2 estimate the error in the integral Z 1 cos ( x ) d x . (c) Calculate the exact value of Z 1 cos ( x ) d x . You may use the substitution x = u 2 . 5. Classify the equation for the di erent values of c given below. You must explain your reasoning. x 2 15-c-y 2 c-6 = 1 ( a ) 6 < c < 15, ( b ) c < 6, ( c ) c > 15. Extra credit ( 5 points ): If f ( x ) = sin ( x 3 ) nd f ( 15 ) ( ) . Good Luck!!!...
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This note was uploaded on 05/01/2008 for the course APPM 1360 taught by Professor Lim,jisun during the Spring '06 term at Colorado.
- Spring '06