a. Explanation Given: The function f ( x ) = 1 − x 2 . Result used: The binomial series for f ( x ) = ( 1 + x ) p centered at 0 is ( 1 + x ) p = ∑ k = 0 ∞ ( p k ) x k , for | x | < 1 . Calculation: The first four nonzero terms of the binomial series centered at 0 is computed as follows, f ( x ) = 1 − x 2 = ( 1 − x 2 ) 1 2 Substitute − x 2 for x and 1 2 for p in ( 1 + x ) p , ( 1 − x 2 ) 1 2 = ∑ k = 0 ∞ ( p k ) ( − x 2 ) k = ( 1 2 0 ) − ( 1 2 1 ) x 2 + ( b. To determine The radius of convergence of the series f ( x ) = 1 − x 2 .

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

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ISBN: 9780134996103

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 11.3, Problem 73E

To determine

To find: The first four nonzero terms of the Taylor series centered at 0 for the given function.

To determine

The radius of convergence of the series f(x)=1−x2.

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Chapter 11.3, Problem 72E

Chapter 11.3, Problem 74E

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↑ Use the following information to complete parts a. and b. below. 3 f(x) = -, a = 1 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. OA. The first four terms are −3+3(x-1)-3(x-1)² +3(x-1)³. OB. The first four terms are 3-3(x-1)+3(x-1)²-3(x-1)³. OC. The first four terms are 3-3(x-1) + 6(x-1)²-9(x-1)³. OD. The first four terms are -3+3(x-1)-6(x-1)² +9(x-1)³. b. Write the power series using summation notation. 3(-1)+1 k=0 (x-1) k 00 Oc. Σ 31-1)*(x-1) k=0 00 OA. OCCER 00 OB. 3(-1)+¹(x-1)* k=0 00 OD. Σ 3(-1)k k=0 (x-1)^ į OWD W

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Chapter 11 Solutions

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

Ch. 11.1 - Verify that p3 satisfies p3(k)(a)=f(k)(a), for k =...Ch. 11.1 - Prob. 2QC Ch. 11.1 - Prob. 3QC Ch. 11.1 - Write out the next two Taylor polynomials p4 and...Ch. 11.1 - Prob. 5QC Ch. 11.1 - Prob. 6QC Ch. 11.1 - Suppose you use a second-order Taylor polynomial...Ch. 11.1 - Does the accuracy of an approximation given by a...Ch. 11.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 11.1 - Prob. 4E

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The first four nonzero terms of the Taylor series centered at 0 for the given function.

Solution Summary: The author calculates the first four nonzero terms of the Taylor series centered at 0 for the given function.

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To find: The first four nonzero terms of the Taylor series centered at 0 for the given function.

The radius of convergence of the series f(x)=1−x2.

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Chapter 11 Solutions