Question
Asked Aug 13, 2019
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For the function f(x) = /x+ 4,find the Taylor series generated by f at x
0.
Choose the correct answer below.
(-1)n+1.1.3.5
. Σ
(2n -3)x"
1
O A. 2+
X
2n.22n-1).n!
n 2
(-1)1-3.5..... (2n + 1)-23-2n)n
Σ
_
O B.
2n. n!
n 0
(-1)" 1-3.5..(2n -3) 41-2n)^"
Σ
X'
O C. 2+
2" n!
n 1
(-1)"1.3.5..... (2n -1)-2(-1-2n)xn
Σ
_
X'
D.
2n n
n 0
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For the function f(x) = /x+ 4,find the Taylor series generated by f at x 0. Choose the correct answer below. (-1)n+1.1.3.5 . Σ (2n -3)x" 1 O A. 2+ X 2n.22n-1).n! n 2 (-1)1-3.5..... (2n + 1)-23-2n)n Σ _ O B. 2n. n! n 0 (-1)" 1-3.5..(2n -3) 41-2n)^" Σ X' O C. 2+ 2" n! n 1 (-1)"1.3.5..... (2n -1)-2(-1-2n)xn Σ _ X' D. 2n n n 0

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Expert Answer

Step 1

Refer to the question, we have to calculate the Taylor series for the provided function,

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f(x)= Vx+4,x=0

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Step 2

Now use the taylors formula to  find the series which is,

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Taylor series, f (x)=f (a)+ a(x-a)+(«(x-a^ +@(x-a+ _ 1! 2! 3!

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Step 3

Then find the derivative of f(x) at x=0 and substit...

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f (0) 0+4 =2 Apply Chain rule, (u) _ df (u) du du dx dx d x+4 dx 1 f'(x) = 2x+4 1 1 f'(0)20+4 4

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Math

Calculus