00 17. Let S = . Verify that for n > 1, n+ yn n+ Jn n+ yn Can either inequality be used to show that S diverges? Show that 2n for n > 1 and conclude that n+ Jn S diverges.

Q: Determine for what values of k the integral ∞∫1dxxk(k>0,k≠1) converges.

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Q: Evaluate the upper sum for f(x) = 1 + cos - ASXST Wwith n = 6.

A: GIVEN: f(x) = 1 + cos (x/2)

Q: Which of the following is TRUE for a, = nr cos(nn) Lütfen birini seçin: a.Diverges and limit does…

A: It can be obtained by using limit evaluation of the given sequence

Q: HW4 Prove the following E R° Jiverges if RE[I, o) and converges if RE[O,I) Hint: Prove |-R

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Q: dr and dz both diverge when p = O a O b O c -1 O d 0.5 O e 1 2.

A: If the limit of integration fails to exist, then the improper integral is said to diverge.

Q: which of the following SSeries Converge 7n 2n2+1, tan

A: Series and sequences

Q: nst. . Decide whether the fo lowing is convergent In the con ver or ०१en1 ९ase ८a्रlवnee ५e 6+1)4"+…

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Q: 6. Consider the integral f(n + 1) = x"e¯* dx where n20. CGive a convincing argument that S* x"e¯*…

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Q: Aw show tha OZ tan (t) is divorges by CL.c.T) Os nol (ntl)2 is converges by CL.c.T) CC.T) 2n+l is…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 2.66 Let fn(x) = z for all r E R. a) Find the pointwise limit of fn. b) Does f converge uniformly on…

A: Convergence and uniform convergence of the sequence

Q: 1.₂0 +00 1 2. Determine whether the integral da converges or rvin x diverges. If it converges,…

A: We have to find out integral

Q: (j) F= R, V = {vER: Un converges as n → ∞0}; (k) F= R, V = {v ER: un converges absolutely as n→ ∞0};…

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Q: [6] 4. Determine the Riemann sum M, using the Midpoint Rule withn=4 in order to approximate the…

A: given expression is ,  using the midpoint rule with n=4 in order to approximate the ,  ∫13(1/x2+2)dx…

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

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

Q: plz ans both B and C

A: This method is called power method. If modulus of all eigen values less than 1 then the power method…

Q: Suppose that X₁, X2, ka)=P(X = _k) =1/2. Let Yn = Xn = n 2 Xi. are independent, such that, for each…

A: Chebyshev's Inequality Chebyshev's inequality guarantees that for a large class of probability…

Q: MEDI is a) converges to 2 b) converges to 2/2 c) converges to 23 d) diverges e) None of all

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Q: Evaluate the following integral or state that it diverges. 00 3dx ,p>1 es XIn Px Select the correct…

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Q: Determine i it convergcs or dverges. Evaloate if converges oo dv 2.

A: We have given,

Q: 13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.

A: givenfn(x)=nx1+n2x2dividing numerator and denominator by x2fn(x)=nxx21+n2x2x2

Q: Write the definite integral for the Riemann sum: 2 (5 + 2)* + (5+ x 2)* + (5 + × 3)*+...+(5 + x n)"|…

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Q: a) Show by example that E( an /b.) may diverge even thagh E an and E bn converge and no b, equals 0.

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: let E an3 be a segence defined recurs ively by An=1 , anti=Jl+5an, n=l,2,3. Suppose that Does { 9n3…

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Q: 16) If E an converges, then cos(am) diverges. n=1 n=1 a) True b) False

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: To compute a* dx using the limit definition, what is the Riemann sum? 1+ 2 n n O 1 9+ 81 n 2 81 1+ 4

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Q: sin(²) En=1 is 18 √n a. 1 b. 12/12 c. Converge d. Diverge d O C O a O b O

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Q: Which of the followings are false? 1. E1 sin converges by comparing with II. E1 T%3D1 nl 00 n-1…

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Q: that you you used to det divergence. 3 n (1). E n5+3 n=1 (1). Σ n 2" n=1

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Q: dx Determine if the improper interal S, xc Fnd it valne if it converges. Conneeges on diree jes.…

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Q: 3 If Xn 4 and ly,l0. Select one: True O False

A: Given, xn → 4  and  yn≤31n2n for all values of n To determine whether ∑ xnynp  is absolutely…

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: Σ Suppose that ax" converges to a function y such that y" – 2y' + y = 0 where y(0) = 0 and y'(0) =…

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Q: 5. Let h, : [0, o∞) → R be given by h„(x) and let h : [0, ∞) → R be given by I +n %3D h(x) = = x.…

A: Answer

Q: Let 1 = S dx c+∞ 4-x I = dx Then I O converges to 3 O converges to .

A: Consider the integral: I=∫1+∞4-xx3dx

Q: Q 12.11 whot values of does this Seirics seines converge? n (in u) n=2

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Q: Consider ax with the given coefficients a,: (2x)" n = 1 ind the radius of convergence R.

A: In this question we will use basic of calculus i.e concept of infinite series. We will use ratio…

Q: (b) For every 3 € R, determine whether the integral 1 dr J V- 1)(1 – 2)*(x – 3)² is convergent or…

A: To check whether the integral is convergent or not, calculate it's limit. if the limit exists, then…

Q: determine the domain AND the function to converge the serie e converge la serie: E=0 Re(u). n%3D0

A: Consider the given series

Q: *show tht the fanetion fW=$- satify The by PotheseI of Rolshe oren- on [0,4]

A: For the solution follow the next step.

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: Using the Nth term test for divergence, 00 n 5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to O 5…

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Q: Set an where r E R is a real number. Prove that ɑn converges to 0 if (-1, 1), cônverges tó 1 if r =…

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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: 00 Determine whether the following integral converges or diverges. 2) Sort (7 (2² + 1)2 dz. QUESTION…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: SELECT ALL A. what condition/s would suffice to ensure A) B) Žaln) S& a(n) S&-Ea(n) converges…

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Q: (b) Use the Weierstrass M-test to show that E(cos.x)". 4 n=0 converges uniformly on [A/4, 37/4].

A: The series is given by: ∑n=0∞cos x2n,    x∈π4,3π4 Now, ∑a2n=a0+a2+a4+... Now, cos function lies…

Q: Ler Flオリ= J a te defiattion of fayler sevies to find the taylor sener of'f"when x- in sigma notation…

A: Given f(x)=1x at x=14

Q: b) Prove that sin z is unbounded in {z E C: |Re z|< 1}. c) Prove that sin- is uniformly convergent…

A: We have to solve given questions.

Q: 3- Let X = R?,x = (x1,x2), y = (y1, Y2) d(x, y) = max {|x1 – y1 |, |x2 – y2 1} If zn = (xn, Yn),…

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Q: a) Show by example thiat E(an /b, ) mey diverge even thagh E an 4nd E b, converge and no b, equak 0.…

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