The series ∑Cn(x+9)^n converges at x=−4 and diverges at x=−17.

Q: 19. Discuss the convergence of the series x²(log 2)9 + x³ (log 3)2 + x^(log 4) +

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Q: Let f(x) = (x − 3)^5 and x0 is not equal to 3. For each n ≥ 0, determine xn+1 from xn by using…

A: To obtain the root of the function fx by Newton-Raphson method, use the following formula.…

Q: p for which In (n) Comvenges

A: Given∑n=1∞ln(n)np

Q: (1). Does the following series converge absolutely, converge conditionally or diverge? (a). Σo(7)".…

A: According to our guidelines, we can answer only the first question or first three subparts of a…

Q: 5. Consider the equation f(x) = x - 2- = 0. (a) Show that the above equation has a solution on the…

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Q: Examine the convergence of the sequence an=sin2n/2n whose general term is (an) Find the limit with…

A: Given sequence is an=sin2n2n. We have to check convergence of the given sequence and then find the…

Q: „(4 - 1) = "p : И

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Q: 3. Find the interval of convergence of the series ☎ n=1 (-1)"+¹(x-2)" 3"-n

A: Find the interval of convergence of the series

Q: (-1)"n" sin" (4) 2n n=1 CS Samed with Camacarner

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Q: 03. Represent f(x)= Tr3x pawer ={ an(x-2)^ as a 4+3X Series Centered at 2.

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Q: 00 The first derivative of the power series f(x) = (-1)" (62)" is n! n=0 O 6 f(x) O f(x) O -6 f(x) O…

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Q: > The sequence {an) is n=1 (i) Converge (ii) Diverge

A: I have proved that sequence has more than one limit points.

Q: The series 0 Cn (x+4)" converges for x = 0 and diverges for x = 3. Circle/indicate the correct…

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Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

Q: The series O True O False Σ (-1)^+1 n=2 n3+1 is absolutely convergent.

A: The given series is summation of (-1)n+1/(n3+1), n from 2 to infinity.

Q: 1. Find a power series representation for the function f(x) = 5x2- Determine the interval of…

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Q: What is the second term in the power series expansion of f(x) = e^x?

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Q: Is the sum from n=1 to infinity of sin(n) convergent, conditionally convergent or divergent?

A: The problem is asking us to determine whether the infinite series ∑n=1∞sin(n) is convergent,…

Q: (a) Show that e /yu dy exists, by considering the series (e/n)". (b) Show that 1 (log n)los n…

A: Given : ∑n=2∞logn-k  and ∑n=2∞logn-n two series where 1st diverges and 2nd converges.  Integral test…

Q: If 2 Cnx" is convergent when x=2 and divergent when x=-3, then 2 Cn is n=0 n =0 convergent. O…

A: Consider the given information: The series ∑n=0∞Cnxn is convergent when x=2 and divergent when x=-3.…

Q: Find the Maclaurin series of tan^−1 (x). Your answer should be in terms of summation notation

A: In the question it is asked to calculate Maclaurin series of tan-1(x) and also it is asked to…

Q: Which of the following information is correct for the sequence 7. 9. dx 1 dx 1 dx 1 dx {an}n=l 5 (a)…

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Q: The first derivative of the power series 3x2 3x f(x) = 3 1! 3x3 3x4 325 %3D - 2! 3! 4! 5! • is

A: Formulae: 1. e-x = 1-x/1! +x2/2! - x3/3! +x4/4!- ....... 2. d/dx{ e-x} = - e-x   Answer: f'(x)= f(x)