a. Explanation Given information: The given function is h ( x ) = 1 ( 1 − x 3 ) 2 . Concept Used: We use the expansion of the function as shown below. g ( x ) = 3 x 2 ( 1 − x 3 ) 2 = 0 + 3 x 2 + 6 x 5 + 9 x 8 + ....... = ∑ n = 1 ∞ 3 n x 3 n − 1 with center and divide it by 3 x 2 . Also, we use ratio test given by Ratio test: Assume that ρ = lim n → ∞ | a n + 1 a n | exists. Then, ∑ a n converges absolutely if ρ < 1 . Then ∑ a n diverges if ρ > 1 . The test is inconclusive if ρ = 1 . Then, radius of convergence is given by 1 ρ . Calculation: As the given function h ( x ) = 1 ( 1 − x 3 ) 2 is the multiple of the function g ( x ) = 3 x 2 ( 1 − x 3 ) 2 , so its power series can be obtained by dividing power series of g ( x ) = 3 x 2 ( 1 − x 3 ) 2 = 0 + 3 x 2 + 6 x 5 + 9 x 8 + ...... b. To determine To find: The expansion of the power series of the given function by squaring the power series of another function which is its root.

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Author: Rogawski

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Chapter 11.6, Problem 43E

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To find:The expansion of the power series of the given function by dividing the power series of another function h(x)=1( 1− x 3 )2 which is its multiple and find its radius of convergence using ratio test.

To determine

To find: The expansion of the power series of the given function by squaring the power series of another function which is its root.

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Chapter 11.6, Problem 42E

Chapter 11.6, Problem 44E

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Chapter 11 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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The expansion of the power series of the given function by dividing the power series of another function h ( x ) = 1 ( 1 − x 3 ) 2 which is its multiple and find its radius of convergence using ratio test.

Solution Summary: The author explains how to find the expansion of the power series of a given function by dividing its multiple and finding its radius of convergence using ratio test.

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To find:The expansion of the power series of the given function by dividing the power series of another function h(x)=1( 1− x 3 )2 which is its multiple and find its radius of convergence using ratio test.

To find: The expansion of the power series of the given function by squaring the power series of another function which is its root.

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Chapter 11 Solutions