A)(sin x)/ is convergent or not B){x} is convergent or not

Q: Find the radius of convergence of in=0 negative infinity -1 infinity

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Q: If dn conditionally converges then Jan| converges. 2=1 2=1 True False Rationale: Reset Selection

A: We have to find the option

Q: converges to 0 Select one: True False

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Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

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Q: converge absolutely, non-absolutel

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Q: 22: Establish the divergence of the sequence x, =(-1)"

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Q: Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. 7 an = sin…

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Q: Prove that or quari -1+ X.- ズい 2. X. ntl converged number Ja to 2.

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Q: Solve the given limit using l'hopitalľ's rule, lim (tan x +1)sinx. (Show your complete solution in a…

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Q: If lim bn pe 0= =1 || En=1 a, converges, then En=1 b, diverges.? True False

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Q: 1 B. Find out if b, where b, = n* sin" 2en -Converges or, -Diverges (Show complete solution using…

A: Given the series is bn=n4sinn12en. Determine whether the series is converges or diverges.

Q: Find the limit of the sequence whose terms are given by a sub n = (n^2)(1 - cos(5.2/n))

A: Given query is to find the limit of the sequence.

Q: Let fn : [-3, 3] → R be defined by fn(x) = x2n x2n+1 Does {fn(x)} converges uniformly on [-3,3]?…

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Q: cos NII 2) Show that converges/diverges.

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Q: Use series to evaluate the limit. sin(3x) – 3x + x3 lim -

A: Given,        limx→0sin(3x)-3x+92x3x5=

Q: cos NII N 2) Show that converges/diverges.

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Q: 5. Explain the extreme value theorem. luouo Ro in Th

A: Extreme value theorm = In calculus , the extreme value theorem states that if a real-valued function…

Q: what is the limit of this sequence limn->Infinity (n*sin(π/n))?

A: The objective is to find limn→∞nsinπn

Q: check if the fixed point itteration converge or diverge for  (6/x-5) in interval [4,5

A: f(x) = (6/x-5)

Q: 5. Suppose that limn00 Tn = 3. Prove directly (i.e. NOT by applying limit laws) that limn→o = 3.

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Q: converges or diverge 2n+ Sin(n)

A: The given series is  ∑n=1∞    12n+sinn We have to check whether the series converges or diverges.

Q: ^2/sin^2(2x-6) = -1 since sinx/x =1? then limit is like x^

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

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Q: Find a sequence X, such that it does not converge to any real number, but Y, does converge to some…

A: Any real sequence Xn is said to be convergent if Xn converging to a unique real number. That is, if…

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: If xi 2, 3dn-1+ 3"n-2 show that {xn} is convergent. identify the limit.

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Q: Use series to evaluate the limit. 4 3 sin(2x) – 2x + lim 4/3

A: Given problem:-

Q: 99. Show that 00 cos x dx is absolutely convergent.

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Q: S sin(n) cos(n)/n converges or 3. Use to sandwich/squeeze theorem to argue whether the sequence 1+n…

A: We need to find if series converges or diverges.

Q: Find the limit of the sequence * a, = ī sin(--), n = 1,2, 3, ... 3

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Q: ∑ ∞ n=1 sin(1/2n) − sin (1/2n + 1). Does this converge or diverge? I believe it diverges by direct…

A: The given series is: ∑n=1∞sin12n-sin12n+1

Q: B. Find out if E bn where bn = n* sin" -Converges or, 2en -Diverges (Show complete solution using…

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Q: Finel Sequence s+ aj sove both limits .

A: Take a sequence, aj=-j2j is rational0j is irrational Then the limit for j rational is,…

Q: (-1)" (2n)! 27 En=1

A: The series is given by ∑n=1∞-1n2n!2n To determine: The convergence of the series using Series Ratio…

Q: (5) Use sequence theorems to prove that lim0 sin() does not exist and that lim,-0 x sin(-) does…

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Q: 4. Prove differentiability implies continuity. Eral

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Q: The radius of convergence (2n + 3)! (x- 1)" is | None of these infinity

A: Given ∑n=0∞(2n+3)! (x-1)n Compare it with ∑n=0∞ an(x-x0)n Then an = (2n+3)!an+1 = (2(n+1)+3)! =…

Q: 4. Determine if the sequence (sin²n+ 2n converges or diverges. Find the limit if it converges.

A: we have to identify the given sequence is convergent or divergent if convergent then find it's limit

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. Зд 2 = sin…

A: topic - sequence and series

Q: prove that if X =CXn) is bounded increasing sequence of real ConVergent and Lim (xu) - Sup [An ineN]…

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Q: Prove that or 「+ X。- ズー 2. 71 number J2 Converged to

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Q: Is there a sequence of continuous functions: fn : [0,1]-->R that is pointwise convergent but the…

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Q: If conditionally converges then Jan| converges. 2=1 n=1 True False Rationale:

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Q: Suppose that p(x)=an" converges on (-1, 1], find the interval of convergen n=0 8 left end included…

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Q: If x1, y1, are two positive unequal numbers and xn = (xn-1+ yn-1)/2 and yn= sqrt(xn-1yn-1)  for all…

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Q: The first term of the mechanic's rule for approximating square roots is a = 1 and it's successive…

A: We have to take limits on both the sides.

Q: If 2 Cnx" is convergent when x=2 and divergent when x--3, then 2 c,5" n = 0 is n= 0 divergent. O…

A: this is inconclusive because if it converges for x=2 than  converges only the values less than 2 but…

Q: Find out if the sequence is convergent or divergent. If convergent, find limit. lim x→∞ cos^2x   /…

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