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Give the 5th degree taylor polynomial for f x lnx1

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Unformatted text preview: centered at 0. Give the 5th degree Taylor polynomial for f (x) = ln(x+1) centered at 0. Give the 5th degree Taylor polynomial for f (x) = cos(x) centered at 0. f ( 2 ) = − 1 , f ' ( 2 ) = 2 , f '' ( 2 ) = − 1 Give the 2nd degree Taylor polynomial for f centered at 2. Rewrite f (x) = 3x3 +2x2 – x + 1 in powers of (x – 2). Create the 3rd degree Taylor Polynomial for f (x) = arctan(x) centered at x = 0. Rn (c) x (x) = ( n + 1) ! f n +1 n +1 Use the Lagrange formula to find the smallest value of n so that the Taylor polynomial of degree n for f (x) = cos (x) centered at x = 0 can be used to approximate f (x) within 10 –4 at x = 1. Which term is truncated if we want to approximate the sum of with an error of less than 1 ? 1000 ∞ ( −1) ∑ 2n 3 n =1 n +1 −1 1. State the indeterminate form and compute the following limits : ln( n + 4 ) a. l i m n →∞ n+2 b. lim ( 3n ) 2 n n→∞ 3⎞ ⎛ c. l i m ⎜ 1 + n →∞ n⎟ ⎝ ⎠ d. lim x →0 2n x − sin ( 2x ) x + sin ( 2x ) e...
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This note was uploaded on 02/01/2014 for the course MATH 1432 taught by Professor Morgan during the Spring '08 term at University of Houston.

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