Test E(-1)" for convergence or 3n+2 divergence.

Q: E(-1)". 9 + In n n=1 Input C for convergence and D for divergence:

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Q: oblem 3. Use the integral test to determine whether Y converges or diverges.

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Q: Define linear convergence?

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Q: Examine the convergence of ,where a>1. (log x)" +1

A: First I have told about Improper integral of first kind and then using it evaluate the given…

Q: If the sequence (xn) convergence to x, then the sequence (Vxn) also .x convergence to

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Q: Test E(-1)" . for convergence or divergence. n2+4

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Q: Use the definition to show that dx 2x2 converges.

A: We have to show that the given integration converges.…

Q: Determine whether each of the fo for convergence/divergence. (a) n +1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: if Xn is bounded, is Xn  cauchy ?  is Xn convergent?

A: Solution

Q: State why the following intergral is improper and find the value if it is convergent: 2r (z² – 4) "

A: The given integral is I=∫262xx2-423dx The integral is improper as the integrand is unbounded at x=2.

Q: 04: A) Discuss the convergence of f,(x) =, , on A-(0, 0).

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Σ-νω( ) 8. (-1)" sin n=1 Input C for convergence and D for divergence:

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Q: By using the substitution t² determine the convergence of = S ∞ dx (x+1)√√x*

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Q: b.),

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Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

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Q: ® Investigate the conurgence of 3. Convergence 2.

A: The given expression is ∑n=1∞n!2en2. We have to find whether the given series is convergent or…

Q: Suppose that anx" converges for x = 5. Must it also converge for x = 4? What about x = -3?

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Q: Find the intervel of tuis function (x-4)" of Convergence n

A: We have to find the interval of convergence of ∑n=1∞ (x-4)nn.

Q: Does sin () x 7 converge or diverge? Why?

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Q: 00 6n–1 Зп+2 1 Apply the nth term divergence test to conclude if E converges or diverges.

A: The divergence of a series can be found using the nth term test. Consider the series . Let . If…

Q: Corver Is absdutely contergent, Conditionally Convergent, on divergent

A: Use Alternating series test, P- series test

Q: Find center, the radius of convergence and interval of convergence for (-1)k+1 (x – 2)* Σ k k=1

A: The radius of convergence is half of the length of the interval of convergence. If the radius of…

Q: Check the convergence of J (x-2)²

A: Let x-2=tThen dx=dti.e.∫-∞11(x-2)2dx∫-∞-11t2dt      [x=-∞, t=-∞-2=-∞]  [When x=1, t=1-2=-1]

Q: +00 2n determine the interval of convergence of (-1)"+1 n3 + 2 n=1

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Q: Prove convergence or divergence.

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Q: A. converges B. diverges

A: Given that the series: A. ∑n=1∞15n B. ∑n=1∞n+6n2+12n+4 To find check the series converges or…

Q: 3. Show that the ratio test is inconclusive, but use either the integral or a comparison test to…

A: Given the series:

Q: Suppose that p(x) = >` anx" converges on (-1, 1], find n=0 the interval of convergence of p(7x – 5)…

A: To find the interval of convergence.

Q: Determine the interval of convergence of n=1 (x - 5)" n²

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Q: 5. Use the Monotonic Convergence Theorem to show that x, converges. (부) -

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Q: What is the difference between formulas of order of convergence O(hk) and these of o(hk)?

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Q: Test (-1)" for convergence or 2n+1 divergence.

A: The given series ∑(-1)n12n2+1

Q: By using the substitution x = t² determine the convergence of d.x [ (x + 1)√x

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Q: Check the convergence of : xe-*dx

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Q: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: Find the interval of convergence of -(x + 10)" n! n=0

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Q: Suppose that p(æ) > anx" converges on (-1, 1], find the internal of convergence of p(6x – 9). n=0

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Q: Test (-1)". for convergence or divergence. 5n2+1

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Q: Use the Root Test to prove convergence or divergence: • (n!)* 2n n=0

A: We have to prove convergence or divergence of given series by root test.

Q: Which test to use and is it convergent/divergent? Σ 16n2 – 8n – 3 n=1 - -

A: Use the ratio test, L=limn→∞an+1an=limn→∞116n+12-8n+1-3116n2-8n-3=limn→∞16n2-8n-316n+12-8n+1-3

Q: E 2 ( – 13" An(n)/2" | .......

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Q: Let                          fn(x) = nx/1 + nx2  (d) Is the convergence uniform on (1,∞)?

A: The given sequence of functions is fnx=nx1+nx2. Compute the limit as follows.…

Q: 8. Suppose ar > 0 and Does > ak converge or k diverge? Why? %3D

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Q: Test the Convergencyo4 Ź tan (hn)

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Q: E(-1)". n! n=1 Input C for convergence and D for divergence:

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Q: Determine the interval of convergence of -1)"+12nx"| n2 + 3

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Q: what is b? it is the same question as a, so what is the convergence of B?

A: We can solve this as follows: