Calculate the Taylor polynomials T2(x) and T3(x) centered at x=9 for f(x)=ln(x+1)

Ayaana Buck

Ayaana Buck

Answered question

2021-09-03

Calculate the Taylor polynomials T2(x) and T3(x) centered at x=9 for f(x)=ln(x+1).

Answer & Explanation

Alannej

Alannej

Skilled2021-09-04Added 104 answers

The given function is f(x)=ln(x+1) and centered at x=9
Find the value of f(9)
f(9)=ln(9+1)
f(9)=ln(10)
Find the value of f(9)
f(x)=d dx ln(x+1)
=1x+1
f(9)=19+1
=110
Find the value of f (9).
f (x)=d dx (1x+1)
=1(x+1)2
f (9)=1(9+1)2
=1100
Find the value of f (9)
f (x)=d dx (1(x+1)2)
=2(x+1)3
f (9)=2(9+1)3
=21000
Obtain Taylors polynomial T2(x) centered at x=9
T2(x)=f(9)+f(9)1!(x9)+f (9)2!(x9)2
=ln10+1101!(x9)+(1100)2!(x9)2
=ln10+110(x9)1200(x9)2
Obtain Taylors polynomial T2(x) centered at x=9
 

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