exercises3 - 2 1 1 x x + + b) Find f (36) (0). Answer: a) 3...

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Exercises - 3 1- Find radius of convergence R and the interval of convergence I of the series 0 (3 2) 3 n n n x n = - Answer: 1 5 , 3 3 I - = & R=1 2- Find a power series representation for f(x) = 1+ x ln 1- x Answer: 2 1 0 2 2 1 n n x n + = + 3- Find sum of the series 2 1 2 1 0 ( 1) 4 (2 1)! n n n n n π + + = - + Answer: 2 2 4- Approximate 0,1 1 e with an error less than 1 1000 5- Find f (100) (0) if f(x) = 2 x e Answer: 100! / 50! 6- a) Find the Maclaurin series for f(x) =
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Unformatted text preview: 2 1 1 x x + + b) Find f (36) (0). Answer: a) 3 (1 ) n n x x ∞ =-∑ b) 36! 7-Find the Maclaurin series for ( ) 2 x f x = Answer: (ln 2) ! n n n x n ∞ = ∑ 8-Evaluate the sum of the series 1 ( 1)! n n n ∞ = + ∑ Answer: 1 9-Find the Taylor series for x about 2. Hint: Write 2 ( 2) x x = +-and use binomial series for (1 ) k x + ....
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