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Chapter 8: Q. 4 (page 692)

If the series 鈭�k=0鈭�bkx-3kconverges to the function g(x) on the interval (鈭�2, 8), provide a formula for bk in terms of the function g.

Short Answer

Expert verified

The formula forbkisfk3k!.

Step by step solution

01

Step 1. Given Information.

The series 鈭�k=0鈭�bkx-3kis converges to g(x)on-2,8.

02

Step 2. Explanation.

The series is converges to the function so, Taylor polynomial for g(x)is in the form role="math" localid="1649488146257" 鈭�k=0鈭�f(k)x0k!x-x0.

For series鈭�k=0鈭�bkx-3k, So,bk=fk3k!

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Most popular questions from this chapter

Is it possible for a power series to have (0,鈭�)as its interval converge? Explain your answer.

Find the interval of convergence for each power series in Exercises 21鈥�48. If the interval of convergence is finite, be sure to analyze the convergence at the endpoints.

鈭�k=0鈭�13k+5kx+3k

In Exercises 41鈥�48 find the fourth Taylor polynomial P4(x)for the specified function and the given value of x0.

45.lnx,3

Prove that if x0鈭�蚁,x0+蚁is the interval of convergence for the series 鈭�k=0鈭�鈥�akx鈭�x0k, then the series converges conditionally at x0+p.

Use an appropriate Maclaurin series to find the values of the series in Exercises 17鈥�22.
鈭�k=0鈭�-蟺kk!
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