V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

Q: 1. Try to use the ratio test or the root test to determine if the following converge or diverge. If…

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Q: an a) Converges n2 b) lim an =0 > cans converges dd) > cos (an) Converges n=1 e) Cos can) diverges

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Q: Σ 1 sin kæ) is uniformly convergent on (-0, 00). Show that k2 k=1

A: In the given question we have to prove that the given series…

Q: ,2 COS“ N cos“ n In n n2 n3 n=1

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Q: Which of the followings are false? 1 1. En-1 sin-| converges by comparing with 2 II. En-1 converges…

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Q: 5a) When p is a real number greater than 1, it can be shown that the improper 1 1 integral |dx…

A: Convergence of Improper Integrals at left-end point: Let us suppose that x=a be the point of…

Q: 00 n-1/2 6 + cos (n) A) diverges B) converges

A: Given series is: ∑n=1∞n-126+cos2n

Q: 1002+x dx Then I J = 1 None of these converges to 1 converges to 2 converges to 3 O is divergent

A: Given I = ∫1∞ 2+xx3dx = ∫1∞(2x-3+x-2) dx = 2∫1∞x-3dx + ∫1∞x-2dx2x-2-21∞ + x-1-11∞= -1x21∞+ -1x1∞=…

Q: 0o Inx dx Evaluate it and state whether it converges or diverges. x2 d)

A: That's easy. Have a good day!!!

Q: cos n! + A) diverges B) converges 3628800

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Q: cos? x+ 1 xp- By using the direct comparison test, the integral 4 x² - 1/2 O Converges O Converges…

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Q: COS n 9. The series > n3 n=1 (a) converges absolutely. (b) converges conditionally. (c) diverges.

A: There are various tests to check the convergence of series. One of test is if a series converges…

Q: 51. For which values of a does eax dx converge?

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Q: sin In(n) A) diverges B) converges 8-1

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

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Q: 4. Let r be a positive number. Determine the value(s) of r, if any, such that converges. As part of…

A: Solution is in step 2

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: For which z's does the infinite series 1+ 좋 + + +. zn + . 3" 27 converge? To what function does it…

A: The solution are next step

Q: M(-1)+ cos?n n= 1 Select one: a. converges absolutely b. converges conditionally C. NOTA d.…

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Q: Σ 4(k!) ² (2k)*! K=( a. Converges completely because re? b. diverges because r=? C. ratio test is…

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Q: n + 3 {Asequence n + 4 Sn=1 converge to e converge to e-lO converge to ei diverge

A: Given:           Sequence ∑n=1∞n+3n+4n     By limit comparison test   If limn→∞anbn=∞ ,then ∑n=1∞bn…

Q: Which of the followings are true? 1. E1 \sin | converges by comparing with -1 II. E1 converges by…

A: Solution: (I) ∑n=1∞sin1n2 We know that sinx≤x Therefore, sin1n2≤1n2 Since ∑n=1∞1n2 converges, thus…

Q: 3n 14 Determine the rate of convergence of the sequence an sin as n → 0. A. O(1/n^2) B. O(1/n^3) C.…

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Q: dx -x 2-x Select one: O a. diverges to -x O b. diverges to x C. converges to -In(6) O d. converges…

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Q: 2+cosx 1. Use the comparison Theorem to determine whether dx is convergent or divergent

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Q: SELECT ALI n! (2n – 1) A) converges by Divergence Test 2 B) a, = 1.3-5 ..... 2n C) diverges by…

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Q: Determine whether E1(-1)" sin n3 is absolute convergent, conditionally convergent, or %=D1…

A: We have to find the series test

Q: 8n 4n2 n = 1 + 1 f(x) = converges O diverges

A: Given query is to find integral converges or diverges.

Q: Represent the function 1x as a power series f(x) = > 2+x n=0 Co C1 = C2 = C3 = C4 = Find the radius…

A: Let gx=x2+x Rewrite the function as  gx=x21+x2

Q: 9. Let a be a positive value. State the integral test, and use this to determine whether ). -an e…

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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: 8+ cos (7x) Perform a test to determine if x converges. 3 n/7 9 dx x3 1/7 (Type an exact answer,…

A: Given integral :

Q: Represent the function as a power series f(x) = > Cnx" 2+ x n=0 Co = 0 C1 = C2 = C3 = C4 = Find the…

A: We have to find power series reptrsentaion as well as radius of convergence:

Q: n! Use the ratio test to determine whether E=1 converges or diverges.

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Q: * 5n' +8n –100 Which of the following tests could be used to determine if 1+2n+n° n=1 converges? I.…

A: The given series is: ∑n=1∞ 5n3+8n-100n3+2n+1

Q: 4 Represent the function as a power series f(x) = (1 — 2г) n=0

A: We know that  (1-x)^n = 1+x + x² + x³ +........ Using this we can solve given problem

Q: The series -1() Lk=1 a ) converge to e b) converge to e-1 c) converge to 1 d) diverge e ) none

A: Given series is ∑k=1∞ k+1kk

Q: *5 dx converges, then which of the following must be true? elect one: 2 a. En-1 converges. O b.p< 0…

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Q: 9. Let a be a positive value. State the integral test, and use this to determine whether > -an e n=0…

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Q: Does ∞ ∑ ((sin^2)(n)/(2^n) n=1 converge or diverge? Use any method and give reasons for your…

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Q: 3k k 18.) Converge or diverge? Explain. Ek=1 5k-1,

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Q: 10.Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.

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Q: 1 [3] b) Determine whether dx converges or diverges. Justify your answer 1+x?

A: According to the question, we have to determine whether ∫0∞11+x2 dx converges or diverges. If the…

Q: n²sinx Show that g„(x) converges uniformly to x e [1,5]. 1+ n²x

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Q: n! +5) A) diverges cos 40320 B) converges

A: We will apply Ratio test to check convergency

Q: 1 -dx x²+2x+5 -00 3n converges to O diverges converges to 3 4 O None converges to 4 converges to

A: Answer is 3π/8.   First option is correct one.

Q: k2 Use the integral test to determine whether 2 1319)2 converges. (k3 + 9)2 k=1

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Q: n1/2 3+ cos (n) A) diverges B) converges Wi

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Q: 1 - dx converges? What are all values of p for which x2p 8.

A: Given : ∫1∞1x2pdx

Q: 2x – x3 1. Evaluate dx. (x – 1)² (x² + 1) 2. Use the previous item to determine if the improper…

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