Homework+26+-+Taylor+Series

Homework+26+-+Taylor+Series - 1 (x)centeredatc=3if a f 3 1...

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Homework 26 – Taylor Series 1) Write out the first four terms of the Taylor series of f(x) centered at c = 3 if a)      3 1 '3 2 ' 12 ' ' 3 ff f f  2) Find the Maclaurin series and find the interval on which the expansion is valid. a)  1 fx x b)     cos 3 x c)     2 sin x d)   25 x fx xe e)  ln 1 5 fx x x  f)   cosh x 3) Find the Taylor series centered at c and find the interval on which the expansion is valid. a) 1 ,1 c x b)   4 31 , 2 x c  4) Use the identity 2 1 cos 1 cos2 2 x x  to find the Maclaurin series for 2 cos x . 5) Identify the function for each of these Maclaurin series. a) 0 n nn n x b) 3 0 1 ! n n n x n
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