Insertar Dibujar Diseño Disposición Referentias Correspohdencia Revisarpri (Cuerpo)V 16K Sae xPárrafoistilosEdiciónDictarEditorAavA AFuenteEstilos NVozEditorFor the function g defined by g(r)1we have1a", for | x| <1.n=0Applying the previous series, the Maclaurin series for the functionfdefined by4f(x):I + 18corresponds to:EG for | x |<1.a)b)for | x | < 18.n=0for | x | <1.c)2.d)1)"18Concentraciónde 18923 palabrasInglés (Estados Unidos)Co ) EN

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Answered: 1 g(x) 1 For the function g defined by…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Consider the series Suppose T-1. lim ky00 TL1 (2₁(-1²) CT CH() X Hint: Consider what happens if k is odd and if k is even.
1. Let A(x) be the series A(x) lowing sequences in terms of compositions and sums involving the expression A(x) (rather than En>o (something). Here is an example: En>o anx". Express the generating series for each of the fol- (Starting with n = 0, the nth term of the sequence is Sequence: -ao, a1, –a2, a3, –a4, a5,.…... (-1)n+lan.) Solution: The generating series for this sequence is given by: E(-1)"+la, *anx" n>0 n>0 = -E an(-x)" n20 = -A(-x) (а) 0, ао, 0, а1, 0, а2, .... (Starting with n = 0, the nth term is 0 if n is even, and a n-1 if n is odd.) (The 0th term is ao, and for all n > 1 the nth term is given (b) ао, а1 + 2ао, а2 + 2а1, аз + 2а2, .... by an + 2an-1.)
3 Consider the function f(x) = For what values of x does the Maclaurin Series for f(x) converge to f(x)? Select 1+4x2 the largest valid interval. ㅇ (-1.1) ㅇ (-1.4) ㅇ (-1,1) O (-1, 1)
Σαπ M n=1 an = Σ n=1 3n+n 6"+In(n) We want to use the limit comparison test to determine whether this series converges or diverges. (a) The dominant term of the numerator is The dominant term of the denominator is We should therefore use b = We get an L= lim n+oo bn == (b) Which of the following statement is true for the series b₁₁? n=1 A. The series diverges by the nth term test for convergence. OB. The series converges by the geometric series test since -1 1. E. The series diverges by the geometric series test since r = F. none of the above >1 (c) What does the limit comparison test tell you about the series A. The test tells us no information OB. The series diverges C. The series converges D. none of the above +∞0 Σ 3" + n¹ 6n+ln(n) ? n=1
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H.W 2/ Answer the following points Find the first three nonzero terms of Maclaurin series for the functions f(x) = e and other function f(x) = e ii. By depending on point (i), find the series for function f(x) = Cosh(x) where Cosh(x) = te Ans/ ) e=1+++ ti) Cosh(x) = 2 e =1- - +1 Cosh(x) = 1+E
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00 1 Use the equation 2x" for |x| < 1 to expand the function in a power series with center c = 0. 1 - x 1- x4 n=0 (Express numbers in exact form. Use symbolic notation and fractions where needed.) Σ 1- x n=0 Determine the interval of convergence. (Give your answer as an interval in the form (*,*). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Usc symbolic notation and fractions where needed.)

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1 g(x) 1 For the function g defined by we have 1 for | x | <1. n=0 Applying the previous series, the Maclaurin series for the functionf defined by 4. f(x) = I + 18 corresponds to: a) 9. EG for | x | <1. 00 b) 6. for | x| < 18. for | x | <1. 18 80 d) for | x | <18. 18 2/9