Q No 2: a) Discuss the convergence and divergence of (1+ a"), Va eR.

Q: - State and prove the convergence order of Newton's approach:

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Q: sin N 8) Show that converges/diverges.

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Q: a) Does f() -Σne" n=0 converge or diverge for r > 0? b) How do you know?

A: According to ratio test, if the limit L<1, then the series converges and if L>1, then the…

Q: Determine the interval of convergence of Σ n=1 (x - 3)" 2T + 1

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Q: Which of the following is correct, for the Mactaurin extensionl of the Function 2x f(x) the…

A: Given fx=∫02xln1+tdt Then  fx=11+t02x=11+2x-1 The Maclaurin series of f(x) is…

Q: нас 2 obtain the Fis for f(x)= X-X² in the interval [-^, ^] ? Solution ht! 2 ans : = = =+ 25 (1452…

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Q: Use the Bolzano-Weierstrass Theorem to show that (Xn) = (1, 3, 5, 7, 1, 3, 5, 7, 1, 3,5, 7, . ....)…

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Q: (-1)"-1 (In n)" 00 23. E n=2

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Q: Determine i absolutely conergent, condifionelly oliverpent. (Do not use the followige serres i's…

A: Don't worry, we will make use of the Comparison test. If the sum of |a[n]| converges, then the sum…

Q: Test the convergency o f Stan ("

A: According to the given information, it is required to test the convergence.

Q: 7. has a fixed point. ) Prove that if f is a continuous function from [2, 5] to [2, 5], then f

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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: 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: CK Show whye* dx does or does not converge.

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Q: 9. The series 3k+ (k+1)* is Convergent Divergent

A: We will solve the following.

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

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Q: Let f (x) = + 2. 5. 131 - 4. 3. 2. On of the theit f(x) following which Interval concate dowr

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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: So I worked out the question. And I got the below setup. And I got the interval of convergence as…

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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: 3. Find the interval fconvergence of the Sevies : 1-3(x-4) + 9 x-4)-..

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Q: (-10) " lon a. Center of convergence b. Radrus of convergence C. interval of convergence {- (x-5)

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Q: Let fn(x) = x^n for x ∈ [0,1]. check if it is pointwise convergence. Define where it becomes…

A: Given, fn(x) = xn , x ∈ [0,1].We will check poitwise convergence of fn on [0,1].

Q: 6 Use ik puer ris 1. 1+X to determine a at o, for FW)-n() poer res Centered the Funchon FW) - I…

A: We have to find the power series representation and radius of convergence.

Q: vergent or Convergent? Identify using any test and state the test used n+2 %3D 2n+7 9n i) En=17…

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Q: 2n+1 4. Use the definition to prove that ) converges.

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Q: If E, 2"an converges and E o(-1)"2"an diverges, then the radius of conver- gence of o anx" is 2.

A: According to the given information, Suppose,

Q: conditions fox which Discuss the fouriex sexies in convergent.

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Q: Question 8 5k„2 k Find the interval of convergence forE (k + 1)? 5 V5 b) O (- V5 V5 V5 d) O e)…

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Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…