Calculate the Taylor polynomials T_2(x) and T_3(x) centered at x=9 for x=9 for f(x)=\ln(x+1)

Bergen

Bergen

Answered question

2021-09-05

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

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-09-06Added 96 answers

Given:
f(x)=ln(x+1)
At x=9,
f(9)=ln(10)
Obtain the derivatives of f(x) follows.
f(x)=1x+1
f(x)=(x+1)2
=1(x+1)2
f(x)=(2)(x+1)3
=2(x+1)3
Compute the values of derivatives at x=9 as shown below.
f(9)=19+1
=110
f(9)=1(9+1)2
=1100
f(9)=2(9+1)3
=1500
Therefore, the Taylor polynomials centered at x=9 is,
T2(x)=f(9)+f(9)1!(x9)+f(9)2!(x9)2
=ln10+110(x9)1100(2)(x9)2
=ln10+110(x9)1200(x9)2
T2(x)=f(9)+f(9)1!(x9)+f(9)2!(x9)2+f(9)3!(x9)3

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?