Explanation Given: The function is ( 1 − x ) 3 4 . Result used: (1) The Binomial series : If k is any number and | x | < 1 then, ( 1 + x ) k can be written as ( 1 + x ) k = ∑ n = 1 ∞ ( k n ) x n = 1 + k x + k ( k − 1 ) 2 ! x 2 + k ( k − 1 ) ( k − 2 ) 3 ! + ⋯ (1) (2) The Ratio Test : (i) If lim n → ∞ | a n + 1 a n | = L < 1 , then the series ∑ n = 1 ∞ a n is absolutely convergent (and therefore convergent.) (ii) If lim n → ∞ | a n + 1 a n | = L > 1 or lim n → ∞ | a n + 1 a n | = ∞ , then the series ∑ n = 1 ∞ a n is divergent. (ii) If lim n → ∞ | a n + 1 a n | = 1 , the Ratio Test inconclusive; that is, no conclusion can be drawn about the convergence or divergence of ∑ n = 1 ∞ a n . Calculation: Substitute − x for x and 3 4 for k in equation (1), [ 1 + ( − x ) ] 3 4 = ∑ n = 1 ∞ ( 3 4 n ) ( − x ) n = ( 1 + 3 4 ( − x ) + ( 3 4 ) ( 3 4 − 1 ) 2 ! ( − x ) 2 + 3 4 ( 3 4 − 1 ) ( 3 4 − 2 ) 3 ! ( − x ) 3 + 3 4 ( 3 4 − 1 ) ( 3 4 − 2 ) ( 3 4 − 3 ) 4 ! ( − x ) 4 ⋯ + 3 4 ( 3 4 − 1 ) ⋯ ( 3 4 − ( n − 1 ) ) n ! ( − x ) n + ⋯ ) = ( 1 − 3 4 x + ( 3 − 4 4 ) 2 ! x 2 − 3 4 ( 3 − 4 4 ) ( 3 − 8 4 ) 3 ! x 3 + 3 4 ( 3 − 4 4 ) ( 3 − 8 4 ) ( 3 − 12 4 ) 4 ! x 4 + ⋯ + 3 4 ( 3 − 4 4 ) ⋯ ( 3 − 4 ( n − 1 ) 4 ) n ! x n + ⋯ ) = ( 1 − 3 4 x + ( − 1 4 ) 2 ! x 2 − 3 4 ( − 1 4 ) ( − 5 4 ) 3 ! x 3 + 3 4 ( − 1 4 ) ( − 5 4 ) ( − 9 4 ) 4 ! x 4 + ⋯ + 3 ( 3 − 4 4 ) ⋯ ( 3 − 4 ( n − 1 ) 4 ) 4 ⋅ n ! x n + ⋯ ) Simplify further and obtain the series, [ 1 + ( − x ) ] 3 4 = 1 − 3 4

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Chapter 11.10, Problem 34E

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To expand: The power series of given function: State the radius of convergence.

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Chapter 11.10, Problem 33E

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

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Chapter 11 Solutions

CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN

Ch. 11.1 - (a) What is a sequence? (b) What does it mean to...Ch. 11.1 - (a) What is a convergent sequence? Give two...Ch. 11.1 - List the first five terms of the sequence. 3....Ch. 11.1 - List the first five terms of the sequence. 4....Ch. 11.1 - List the first five terms of the sequence. 5....Ch. 11.1 - List the first five terms of the sequence. 6....Ch. 11.1 - List the first five terms of the sequence. 7....Ch. 11.1 - List the first five terms of the sequence. 8....Ch. 11.1 - Prob. 9E Ch. 11.1 - List the first five terms of the sequence. 10. a1...

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To expand: The power series of given function: State the radius of convergence.

Solution Summary: The author explains how the power series of given function is (1-x)34 and the radius of convergence is 1.

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Chapter 11 Solutions