   Chapter 11.8, Problem 36E

Chapter
Section
Textbook Problem

The function A defined by A ( x ) = 1 + x 3 2 ⋅ 3 + x 6 2 ⋅ 3 ⋅ 5 ⋅ 6 + x 9 2 ⋅ 3 ⋅ 5 ⋅ 6 ⋅ 8 ⋅ 9 + ⋅ ⋅ ⋅ is called an Airy function after the English mathematician and astronomer Sir George Airy (1801–1892).(a) Find the domain of the Airy function.(b) Graph the first several partial sums on a common screen.(c) If your CAS has built-in Airy functions, graph A on the same screen as the partial sums in part (b) and observe how the partial sums approximate A.

To determine

(a)

To find:

The domain of the function

Ax=1+x32·3+x62·3·5·6+x92·3·5·6·8·9+

Explanation

1) Concept:

The given series is

Ax=1+x32·3+x62·3·5·6+x92·3·5·6·8·9+

=1+n=1x3n2·3·5···········3n-13n

=1+n=1k=1n(3k-2)3n!x3n

So, apply the ratio test and find the interval of convergence.

2) Given:

Ax=1+x32·3+x62·3·5·6+x92·3·5·6·8·9+

3) Calculation:

The given series is

Ax=1+x32·3+x62·3·5·6+x92·3·5·6·8·9+

=1+n=1x3n2·3

To determine

(b)

To sketch:

The graph of several partial sums of this series

To determine

(c)

To sketch:

The graph of J1 and the partial sums as in part (b) on the same screen using CAS

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