Find the nth Taylor polynomial centered at c. f(x)=1/x^{2}, n=4,

ukelangf0

ukelangf0

Answered question

2021-12-04

Find the nth Taylor polynomial centered at c. f(x)=1x2,n=4,c=2

Answer & Explanation

Tamara Donohue

Tamara Donohue

Beginner2021-12-05Added 11 answers

We need to find the 4th Taylor Polynomial for the function f(x)=1x2 centered at c=-2. Therefore, we need to caclulate f(2.1),f(2.1),f(2.1),f(4)(2.1).
f(x)=1x2
f(x)=2x3
f(x)=6x4
f(x)=24x5
f(4)(x)=120x6
f(2.1)=1(2.1)2=14
f(2.1)=2(2.1)3=14
f(2.1)=6(2.1)4=38
f(2.1)=24(2.1)5=34
f(4)(2.1)=120(2.1)6=158
Therefore, the 4th Taylor Polynomial is
P4(x)=14+14(x+2)+382!(x+2)2+343!(x+2)3+1584!(x+2)4
Result:
P4(x)=14+14(x+2)+382!(x+2)2+343!(x+2)3+1584!(x+2

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