Find the Taylor polynomial of degree n=4 for each function expanded about the given value of x_0 f(x)=cos(x), x_0 =0

Lilliana Livingston 2022-07-27 Answered
Find the Taylor polynomial of degree n=4 for each function expanded about the given value of x 0 .
f ( x ) = cos ( x ) , x 0 = 0
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Answers (1)

Bradley Sherman
Answered 2022-07-28 Author has 17 answers
f ( x ) = f ( x 0 ) + x f ( x 0 ) 1 ! + x 2 f ( x 0 ) 2 ! + . . .
f ( x ) = cos 0 = 1
f ( x ) = sin x f ( 0 ) = sin 0 = 0
f ( x ) = cos x f ( 0 ) = cos 0 = 1
f ( x ) = sin x f ( 0 ) = sin 0 = 0
f ( i v ) ( x ) = cos x f ( i v ) ( 0 ) = cos 0 = 1
f ( v ) ( x ) = sin x f ( v ) ( 0 ) = sin 0 = 0
f ( v i ) ( x ) = cos x f ( v i ) ( 0 ) = cos 0 = 1
so on
f ( x ) = 1 x 2 2 ! + x 4 4 ! x 6 6 ! + . . . . = n = 0 ( 1 ) n x 2 n ( 2 n ) !
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