Section10.3.pdf - TAYLOR SERIES(10.3(practice 1 The...

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TAYLOR SERIES (10.3) (practice) 1. The following parts refer to 1 ( ) 3 f x x = . A. Write the Taylor series expansion for ( ) f x about x = 0. B. Find the Taylor series expansion for ( ) f x about x = 2 without actually taking the derivatives. (Hint: rewrite the denominator so that 2 x appears.) C. Use part A to find each of the following (0) f (0) f ′′′ ) 0 ( ) 5 ( f D. Use part B to find each of the following (2) f (2) f ′′′ (5) (2) f 2. Find the exact value of the following sums: A. + + ! 8 ) 2 . 0 ( 5 ! 6 ) 2 . 0 ( 5 ! 4 ) 2 . 0 ( 5 ! 2 ) 2 . 0 ( 5 5 8 6 4 2 B. + + ! 7 ) 2 . 0 ( ! 5 ) 2 . 0 ( ! 3 4 ) 2 . 0 ( ) 2 . 0 ( 8 6 2 C. 2 4 6 8 5(0.2) 5(0.2) 5(0.2) 5(0.2) 5 1! 2! 3! 4! + + −⋅⋅⋅ D. + + + 2 ) 2 . 0 ( 5 2 ) 2 . 0 ( 5 2 ) 2 . 0 ( 5 2 ) 2 . 0 ( 5 8 6 4 2 3. Use series to evaluate the limit 2 0 arctan( ) lim 1 x x x x e . 4. Expand 2 2 ) ( h R mgR F + = in terms of R h . Assume R is very large when compared to h . 5. Expand ( ) R a R Q + = 2 2 2 πσ in terms of R a . Assume R is very large when compared to a .
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