Calculate a 3rd order Maclaurin series phi( х ) = ( 1 + х)^(1 / х),

skilmarka8j 2022-09-26 Answered
calculate a 3rd order Maclaurin series
f ( x ) = ( 1 + x ) 1 / x ,
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Answers (1)

Lorenzo Acosta
Answered 2022-09-27 Author has 13 answers
ln ( 1 + x ) x = 1 x 2 + x 2 3 x 3 4 + o ( x 3 )
Substitute x 2 + x 2 3 x 3 4 to u in the development of e u , first computing the succesive powers of u
u 2 = x 2 4 x 3 3 + o ( x 3 ) , u 3 x 3 8 + o ( x 3 ) ,
so that
( 1 + x ) 1 x = e ( 1 + u + u 2 2 + u 3 6 + o ( u ) ) = e ( 1 x 2 + 11 48 x 2 7 16 x 3 + o ( x 3 ) ) .
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