1010 Calculate the Maclaurin series for x x f 2 1 to the 3 term Solution 8 3 16

1010 calculate the maclaurin series for x x f 2 1 to

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. (10.10) Calculate the Maclaurin series for x x f 2 1 ) ( to the 𝑥 3 term Solution: 8 3 16 6 ) 0 ( ' ' ' , ) 2 ( 6 ) ( ' ' ' ; 4 1 ) 0 ( " , ) 2 ( 2 ) ( " ; 4 1 ) 0 ( ' , ) 2 ( 1 ) ( ' ; 2 1 ) 0 ( 4 3 2 f x x f f x x f f x x f f 3 4 2 3 2 3 2 3 2 ) ( 3 2 0 ) ( 2 1 2 1 2 1 2 1 16 1 8 1 4 1 2 1 6 8 / 3 2 4 / 1 4 1 2 1 ! ) 0 ( ! 3 ) 0 ( ' ' ' ! 2 ) 0 ( " ) 0 ( ' ) 0 ( ! ) 0 ( 2 2 x x x x x x x x x x n f x f x f x f f x n f x n n n n n Further Discussion: The last formation is not necessary but it tells us that the general form k k k k x x f 0 1 2 1 ) 1 ( ) ( and its Maclaurin series k k k k x x 0 1 2 1 ) 1 ( 2 1

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