Section 6.1 p. 542/544 # 18 In the following exercises, find the radius of convergence R and interval of converge for Ea,x" with the given coefficients a,. ,k°x* 18. k=1

Q: 1. Let z, be the sequence of approximations to the root of f(x) = 0 and r, is a suitably close…

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Q: 3. Use the Test for Divergence to explain why if En-0 an converges, then En=0 am must diverge.

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Q: enn! n→∞ nn+1/2 (b) It is known that lim = √2. Verify this numerically.

A: To find the limit limn→∞enn!nn+12 proceed as follows. According to the Stirling's approximation…

Q: 7) The point p = 3 is a zero of the function f(x) = x³ - 7x2 + 15x - 9, using Newton iteration to…

A: Differentiate the function fx=x3-7x2+15x-9 with respect to x, to find the derivatives f'x and f''x.…

Q: The causal sequence {x} Xg = (G)* (k> 0) %3D XK Determine the z transform

A: given                                                xk=12k; (k≥0) we have to find z-transformation.…

Q: Theorem 64. Let {pk}1 converge to point If y # x, then {pk}1 does not converge to y. x.

A: Given that sequence pkk=1∞ converges to point x.

Q: Use the root test to determine whether >a, converges, where An is as follows. n=1 332. a, = n/ e"

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Q: 1 1 3. Find the sum of the following convergent series: 2" (п+1Xn+2)

A: As you didn't mention the question numberto be solved so i solved First  question.For remaining…

Q: Question 15 Find the interval of convergence for (k+ 2)! (x – 9)*+4 - а) О(-9,9) b) O{9} c) O(-0,…

A: Solve the following

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

A: Given series is: ∑n=1∞n-126+cos2n

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (2n-1)!] a)…

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Q: Σ +1 n=1 (-1)*-1(x-1)" nat

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Q: (x + n)² Show that h„(x) converges poimtwise to f(x) = 1, V x e [1, 00). %3| x² + n²

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Q: The following four methods are proposed to compute 213. WRITE them in order, based on their apparent…

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Q: 1. Let D = the sales of DVDs in billions of dollars, S = the total sales of streaming videos in…

A: The sales of dvds given as the function D = -0.92t + 8.75 and the total sales of streaming videos…

Q: Prove that the sequence xn has a convergent subsequence. 3n4 sin n – 4n cos n2 + 2 a) Xn 5n4 – 8n –…

A: We have to prove that xn has a convergent subsequence in each of the given cases.

Q: re 1. (a) Let fn(x) = (1-x)x". Prove that the sequence converges point-wise on [0,1]. Find the limit…

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Q: 5η X b) Σπ n! n=0 8

A: Given series is ∑n=0∞x5nn!

Q: Exercise 2. Determine whether the sequence of functions (fn)n converges uniformly on S. fn(x) = nx"…

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Q: · (−1)″ √2n+ 5 n³ +2n +4 n=1 t) Å sin(n) 3 n

A: Given series are: s) ∑n=1∞-1n2n+5n3+2n+4                            t)  ∑n=1∞sinnn3 To prove: Test…

Q: Exercise 2.4.3. (a) Show that V2, y2 + v2, V2+ V2 + v2,... converges and find the limit. (b) Does…

A: (a) Given sequence is 2, 2+2, 2+2+2,..... We have to show that the sequence 2, 2+2, 2+2+2,..... is…

Q: Let f(r) = 15x + 6a? – . Can Golden Ratio search method be used to find a local minimum of f…

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Q: Question 3 Find the interval of convergence for (k + 2)! (x – 3)* а) О(-0о, о) b) O {3} с) О (2,4)…

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Q: 2n zn こ (n) n:0

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Part C

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Q: B3.3.4.1f) (1) Use limit laws and SL. 1 - SL. 8 for sequences, to evaluate the following limits: cos…

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Q: SntXn stx

A: We have to test the convergency.

Q: (x – 2)" is: The radius of convergence of 2 n=1 (3)"n² .1 5 .2 7 .3 3 .4 4

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Q: en k%3D1 00

A: We will use Cauchy root test

Q: 1 5. Determine by the limit comparison test if Zn=2 converges or diverges. Vn-1

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Q: 1 Prove: Ex-1 n=1 (n+1)(log(n+1)), converges for p > 1 and diverges for p ≤ 1.

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Q: Use the definition of convergence to prove lim COS n 72-00 n²n+1 = 0 || -

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Q: Prove that a sequence (Xn)neN of vectors in Rd converges if and only if each one of the sequences…

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