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Unformatted text preview: X n =1 (1) n +1 ( n √ e1) 2. (10 points) Find the secondorder Taylor polynomial of the function f ( x ) = 3 √ x near x = 8. Compute the approximate value of 3 √ 10 given by this polynomial. (Leave your answer in fraction form, but simplify it.) 3. (8 points) For which values of x does the power series ∞ X n =2 ( x4) n n ln 2 n converge? Justify your answer. 4. (10 points) (a) State (or compute) the Taylor series centered at 0 of f ( x ) = ln(1 + x ). (b) State (or compute) the Taylor series centered at 0 of g ( x ) = 1 1 + x 2 . (c) Compute the ﬁrst four nonzero terms of the Taylor series centered at 0 of h ( x ) = ln(1 + x ) 1 + x 2 . 5. (10 points) Compute the following limits: (a) lim x → sin 3 x (1cos 2 x ) e x 31 (b) lim x →∞ x 2 ± e1 /x 21 ²...
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This homework help was uploaded on 02/12/2008 for the course MATH 104 taught by Professor Nelson during the Fall '07 term at Princeton.
 Fall '07
 Nelson
 Power Series, Taylor Series

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