Taylor polynomialsa. Find the nth-order Taylor

Chapter 7, Problem 20E

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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.

\(f(x)=\sin ^{-1} x\)

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.

\(f(x)=\sin ^{-1} x\)

ANSWER:

Solution 20E

Step 1:

A Taylor series of function f(x) at a is defined as :-

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