?(a) Find the Taylor polynomials up to degree 5 for \(f(x)=\sin x\) centered at \(a=0\)

Chapter 11, Problem 1

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QUESTION:

(a) Find the Taylor polynomials up to degree 5 for \(f(x)=\sin x\) centered at \(a=0\). Graph f and these polynomials on a common screen.

(b) Evaluate f and these polynomials at \(x=\pi / 4, \pi / 2\), and \(\pi\).

(c) Comment on how the Taylor polynomials converge to f(x).

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QUESTION:

(a) Find the Taylor polynomials up to degree 5 for \(f(x)=\sin x\) centered at \(a=0\). Graph f and these polynomials on a common screen.

(b) Evaluate f and these polynomials at \(x=\pi / 4, \pi / 2\), and \(\pi\).

(c) Comment on how the Taylor polynomials converge to f(x).

ANSWER:

Step 1 of 4

(a)

Write the Taylor polynomial with  for term up to  as follows.

Similarly, calculate the lower degree of Taylor polynomials.

                                                                   

And,

                                                                   

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