Answer: Taylor polynomialsa. Find the nth-order Taylor

Chapter 7, Problem 15E

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QUESTION:

Taylor polynomials

a. Find the nth-order Taylor polynomials of the given function centered at 0 for n = 0, 1, and 2.

b. Graph the Taylor polynomials and the function.

f(x) = In (1 – x)

Questions & Answers

QUESTION:

Taylor polynomials

a. Find the nth-order Taylor polynomials of the given function centered at 0 for n = 0, 1, and 2.

b. Graph the Taylor polynomials and the function.

f(x) = In (1 – x)

ANSWER:

Solution 15E

Step 1 :

Given

(a).We are asked to find the order polynomial  with  and  for

The taylor polynomial is generally given by

In this question it is

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