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

Q: a, n = n 3n+1 3n-1 A) convergence C) test fails B) divergence O ооо

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Q: 2. Zい(n+2)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2 1 dx 8 dx 1 dx 1 dx 2 X 6 8 X 1 which one is true? (a) {an} diverges to +o (b) {an} diverges to -o…

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Q: Let fn RR be a sequence of continuous functions which converg uniformly to a function f : R → R. Let…

A: see my solution

Q: how that fuGe)= x" (1-x") converges bintwise # se G, 1]. Is fn G) Thyenges %3D uni formly?

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Q: (n²)(1 - cos(뉴)). 1.5 COS An

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Q: O4l determine if the geometric series converges o diverges o If seri es converg es, find its sum 3.…

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Q: sin sin A) converges B) diverges

A: Recall: Telescoping Series Test:      Telescoping series are of the form…

Q: Question # (5 1: Determine if convergent or divergent: 1 4 9" 5 A) Divergent B) Convergent C) Can…

A: option A is correct. see 2nd step.

Q: ΣΕΠλη της 9 - 515 +1 _h=1

A: The series is given asAlternating series test -Suppose that we have a series  or  where  for all n.…

Q: If an diverges and 0 (-1)"an converges. n=1 B)>(-1)"b, converges. n=1 c) 2(-1)"bn diverges. n=1 D b,…

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

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Q: of the given improper in tegrals convergent. are sinz da 1. ース? de

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Q: Solve Σ 0 to ∞ ((n! • x^n)/ n^n) for x = e and x = -e and explain whether each point converges or…

A: Solve for x = e and check whether it converges or diverges as follows.

Q: Given ſtan xdx = limn→∞ Σ-1 (tan 7)) (7) identify if it is a right k=1 Riemann sum. O True O False

A: The right Riemann sum of integral

Q: 00 Let r be a constant. Suppose ' converges to -1, then the sum of )r' is i-1 i-0

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Q: 8n Show that fn (x) = x2" – x" is unfiormly converges or not by using uniform norm

A: The given function is  fn(x)=x2n-x8n We show that the function is uniformly converges or not by…

Q: x +x2+..+ xn Let 0 is convergent, show that is convergent or divergent (2)Let is convergent, show…

A: (a) Given that an=x1+x2+...+xnn, bn=x1x2...xn1n It is known that bn≤an Since an is convergent. By…

Q: using agraph comparison te ot explain continouw on T0,00) and lim fead=l, Is it 2900 possible theu…

A: We can evaluate an exact value of a definite integral. But, for improper integral, we can't evaluate…

Q: Let fn(x) = sin" x and let 8 > 0. a) Prove: fn converges uniformly on [0, 5 – 8], but not uniformly…

A: The given function is fnx=sinnx. To find: (a) fnx=sinnx uniformly or not on given domains.…

Q: SELECT (n!)? (2n)! .()* B) is similar to G A) converges C) is similar to )" D) diverges

A: We will use Ratio Test to determine convergency

Q: з Σ (-1)^ hai боu итиеть n ди

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Q: g) an = In(n+ 1) – In(n) (Hint: simplify the logarithms) (-3)" h) an n! i) an = Vn + 2 – V2n

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Q: of Eca 4 is cenvengend can we conclude that cach of these are convergent: (b) E cn (-4)^ ca)

A: Given that ∑n=0∞Cn4n is convergent.

Q: Exercise 6. Let (an) be the sequence Sao d Ants = 20²0. an +1 Let α = = 42 defined by = and show…

A:

Q: Study uniform convergence on 10, 1) of the sequence of functions Jn for the following: a fn(x) =…

A: Solution a: Given that fn(x)=11+(nx+1)3 in 0,1. Now, f(x)=limn→∞fn(x)=limn→∞11+(nx+1)3=0,    x≠012,…

Q: Consider sequences (– 1)"n (i) Зп — 1 (1) cos T- (ii) n2+ 3n (iii) Зп2+ 5 n Which of the following…

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Q: Show that a sequence of Riemann-Integrable functions fn(x) converges uniformly to Riemann-integrable…

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Q: does the sequence an converge or diverge? Find the limit if the sequence is convergent…

A: givenan=cos(3pi2 - 6n)

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: (x – 3)" which one are true? n=1 I: divergent for x = 5 II:Conditionally convergent for x = 2 III :…

A: 17. I. is true.

Q: n - 1 converges absolutely because lim - 2 (n – 1) R=1 True O False Reset Selection

A: Consider the given series.

Q: e{3k(n +7) sin( 1. -) +7} k(n+7)

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Q: Prove that these two E E cos (Tin) não Inn 2 are تم 22=1 convergent (-1) h 22²41

A: A series is defined as the combination of the sequence. A series is said to be convergent when n…

Q: Let (fa). be a sequence of functions f : [0, 1] Rdefined by fa(z) = S2n²z +1 if z<! %3D Then 1. S.)…

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Q: O (*+n)* Given fafx)= x*+n?' find NeN such that fu (x) converges to f(x) =1 Vx e [,-) a) E c) d)…

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