Find the limit and the rate of convergence of the following sequence as h → 0 : sin h lim h cos h h2

Q: In the usual notation, state the Dirichlet test for a functional sequence. Hence show that each of…

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Q: sin²n'

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Q: I need To find a Sequence of functions (m c^(E-!, 13) That is cavchy Cuith Il ) and does not…

A: Given: C1-1, 1 To find: A sequence of functions in C1-1, 1 which is Cauchy but not convergent in…

Q: Find the radius of convergence and interval of convergence of the se 10" " n2 n=3 R = = [[ +

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Q: Determine the rate of convergence of the sequence an = sin( as n + 00. A. O(1/n) B. O(n) OC.…

A: given sequence an=sin2n+3n2-5  to find the rate of convergence of sequence as n→∞

Q: The sequence an =n-Vn +1vn+3 converges to the limit A)-3 B) -1 C) 1 D) +2 E) -2 F) 0

A: Given:

Q: f,(z) = 1+ 1+ nz

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Q: Find the radius of convergence for: 3"r" n!

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Q: The sequence ɑn = 1 + converges to the limit A) e B) ve C) Ve D) e? E) F) e? /2

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Q: Calculate the Radius and the Interval of Convergence na" 2n n=0

A: we will be using ratio test for the series to converge.

Q: Find the limit for the following sequences and determine their convergence: In n (-4)" n! i) an =…

A: Given  1) an=-4nn!       2) an=lnnn1/n     3) an=n-n2-1

Q: If Cn(x – 3)" converges at z = 7 and diverges at z = 12, what can you say about: (a) the convergence…

A: Given that ΣCn(x-3)n converges at x=7 and diverges at x=12. We know that, if the power series is…

Q: a) For which values of x does f(x) =E n=0 converge and for which values ofx does it diverge? b) When…

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Q: Let f(r ) Σr" n=1 a. Determine the interval of convergence for f. b. Let g(x) = f(x)/x. Find an…

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Q: Find the rate of convergence of the following sequence as n → 0o. n +1 lim 1 400 n +2 -1

A: In this question, the concept of rate of Convergence is applied. Rate of Convergence The rate of…

Q: Find the radius of convergence for E, (11/ 5)" 2n

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Q: Show that the sequence {fn} where fu(r) = e-n* is uniformly convergent on [a, b), a > 0.

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Q: Find the radius of convergence, R, of the ser (-1) R =

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Q: O Find the interval of convergence for the following power seu * (x +3)"

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Q: / Find the limits of the following sequences and determine their convergence? an = n(1-cos — )

A: here I am using expension of function and then find the limits.

Q: Find the radius of convergence for zn/n , n = 1 to infinity.

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Q: Find the limit for the following sequences and determine their convergence (-4)" In n i) a, ii) a =…

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Q: Compute the point-wise limit of (fn) and determine if they converge uniformly on given intervals. 1.…

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Q: Consider the sequence of functions {fn}nen, where nx fn(z) = Va € [1, 10]. 1+ nx' (a) Find the…

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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: Find the radius of convergence for: 5"z" Σ n!

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Q: Find the radius of convergence for: (n!)°a" (2n)! n=1

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Q: Find the radius of convergence and the interval of convergence for the following. (а) (z+1)" n=1

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Q: Vn cos(nle") n +1 (n + 1)" (а) ап (b) b, = (c) Cn = 2n sin n nn+1

A: The given sequences area) an=ncosn!enn+1b) bn=(n+1)nnn+1c) cn=2nsinπn

Q: State whether the following converge as n → 00; if yes, find the limit. Justify your answer. (а)…

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Q: Determine if the following sequence converges or diverges and find the limit if possible. Sin(n+ 1)…

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Q: Let fn(x) x +n b. Use the Lemma for non-uniform convergence to show that the sequence does not…

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Q: Given two sequences (fn)neN, (9n) nEN C C[0, 1] of continuous functions on the closed unit interval…

A: Given two sequences fn, gn contained in the interval 0,1 of continuous function on 0,1 by…

Q: State whether the sequence an = Vn +7 converges and, if it does, find the limit. a) O converges to…

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Q: Determine the following by using an appropriate Riemann sum. lim ... + n] 1? + 2 + 32 + n → 0 n-

A: Limit.

Q: (a) Define Vn E N, an rate constant for which this sequence converges to 0. – 3-" +. Find the order…

A: Given that, ∀n∈ℕ, xn=1n2n-3-n+1nn We have to prove that xn converges to 0.

Q: Ln=0*

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Q: uniformly co

A: Given, if fn and gn are uniformly convergent sequences of functions. To prove that fn+gn converges…

Q: Given f: [2, )IR, prove that fn (x) = けx" It, converger uni formly to f6)-o.

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Q: Consider the convergence of the sequence X = (Xn), where 1 1 1 Xn for n € N. n + 1 n + 2 2n

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Q: 1 dx where p> 1 %3D xP

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Q: To compute a? dx using the limit definition, what is the Riemann sum? 2 3 + 2+

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Q: The sequence a=n-vn+1Vn+3 converges to the limit A) -3 B) -1 C) 1 D) +2 E) -2 F) 0

A: For a series ; if it converges then . If  the limit ; then the series diverges.

Q: Use the ratio test to find the radius of convergence for En (z - 3)". n=0

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Q: Determine the values of p for which f(x)da converges where f(x) = = 1-e-z TP

A: Here, in the question for what value of p the integral is convergent. The simple improper integral…

Q: Consider the sequence defined by xo = a > 0 and %3D a X+1 = } ( x* + -) Xk Prove that this sequence…

A: Rate of convergence: Assume we have a series of real numbers that all converge to x. x0, x1, x2,...,…

Q: (e) $₁ = 5 and Sn+1 = √√4s +1 for n ≥ 1.

A: Given s1 = 5 and sn+1 = 4sn+1 for n≥1

Q: The interval of convergence of +o B(x+7)“ is

A: Given, ∑n=0∞8(x+7)n3n

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.