Find the MacLaurin polynomial for f(x)=1/(1+5x^3) by substituting -5x^3 for x in the Maclaurin polynomial of 1/(1-x).

nazismes2w7

nazismes2w7

Answered question

2022-11-26

Find the MacLaurin polynomial for f ( x ) = 1 1 + 5 x 3 by substituting 5 x 3 for x in the Maclaurin polynomial of 1 1 x

Answer & Explanation

Beckham Krueger

Beckham Krueger

Beginner2022-11-27Added 7 answers

Given that f ( x ) = 1 1 + 5 x 3
The Maclaurin polynomial of 1 1 x is
1 1 x = ( 1 x ) 1 = 1 + x + x 2 + x 3 + . . . + x n
1 1 + 5 x 3 = 1 1 ( 5 x 3 ) = ( 1 ( 5 x 3 ) ) 1 = 1 + ( 5 x 3 ) + ( 5 x 3 ) r + ( 5 x 3 ) 3 + . . . + ( 5 x ) n = 1 5 x 3 + 25 x 6 125 x 9 + . . . + ( 5 x 3 ) n T 3 n ( x ) = 1 5 x 3 + 25 x 6 125 x 9 + . . . + ( 5 x 3 ) n

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