Unformatted text preview: ∞ X n = 1 (2 ) n √ n ( x + 3 ) n 3. (a) Write f ( x ) = x ( 1x ) 2 as a power series. (b) Substitute x = 1 2 in your answer in part (a) and thus, or otherwise, ﬁnd ∞ 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 1x 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 ﬀ erent values of c given below. You must explain your reasoning. x 2 15cy 2 c6 = 1 ( a ) 6 < c < 15, ( b ) c < 6, ( c ) c > 15. Extra credit ( 5 points ): If f ( x ) = sin ( x 3 ) ﬁnd f ( 15 ) ( ) . Good Luck!!!...
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 Spring '06
 LIM,JISUN
 Calculus, Power Series, Taylor Series, Mclaurin

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