Chapter 11.10, Problem 15E
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Multivariable Calculus
8th Edition
James Stewart
ISBN: 9781305266643
Solutions
Chapter
Section
BuyFindarrow_forward
Multivariable Calculus
8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence.
15. f(x) = 2x
To determine
To find: The Maclaurin series for
Explanation
Given:
The function is
Result used:
(1) "The expansion of the Maclaurin series
(2) The Ratio Test:
“(i) If
(ii) If
(ii) If
Calculation:
Obtain
Substitute 0 for x in
Find the first derivative of
That is,
Substitute 0 for x,
Find the second derivative of
Simplify further and obtain
Find the third derivative of
Simplify further and obtain
Find the fourth derivative of
Chapter 11 Solutions
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