Corollary 11.2.8. IfΣanx" converges pointwise to f on an interval containing 0 and æ and En=1 annx" containing 0 and x, then f'(x) = 1 annxn-¹. converges uniformly on an interval n-: in-context

Q: 28.P. Let f. (x)= |x]*1f for x in [-1, 1]. Show that each f. is differentiable on [-1, 1] and that…

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Q: 2. Zい(n+2)

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

Q: Which of the followings are true? 1.En=1 7?+Inn (-1)" is absolutely convergent. II. >n=1 (-1)m is…

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Q: 27. The graph of a function f is given. Let F(x)=f(1)dt = f(1)dt_then for 0 0<x<2 F(x) is: [A]…

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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: uppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given…

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Q: 3. (a) Let an max{sin 1, sin 2, sin 3,... sin n} Does {an} converge? What is its limit? Explain. =

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Q: 10 TJC Promo 9740/2006/Q6 A geometric progression has first term a (where a > 0), and common ratio…

A: Sum of the first n terms is given as

Q: Give an example of a sequence of differentiable functions {f_n: (-1,1)—>R} that converges uniformly…

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Q: of the given improper in tegrals convergent. are sinz da 1. ース? de

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Q: 10. Give an example that Xn X but Xn does not converge to X in probability.

A: 10. Let Xn=-X, for n=1,2,3,... where X~N(0,1). Now, the CDF of Xn is FXn(xn)=PXn≤xn, for xn∈ℝ and…

Q: 11) If X be a r.v. from exponential distribution (x)= e- ス>0, x20 Then the moment generating…

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Q: Question The below figure represents a graph of the function f on the interval |-,n). The iterations…

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Q: Let an > 0 and assume that an diverges. Write Sn = a1 + a2 + • ·.+ an. Prove the following…

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Q: 34. Assume that an+1/an converges to p = 4. -1 Does > an converge (assume that n=1 An # 0 for all…

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Q: 1.1 Determine whether the sequence {f.(x)} = {; on I = [0, 1]. converges uniformly %3D

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Q: that (An) rges in babilit to A II ntains a further subsequence that converges a.e. to X. only if…

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Q: Q.2) Determine of each point convergens or diverges: (-1)"(3n)!/ /n! (n + 1)! (n+ 2)!

A: determine whether the series converges of diverges (i) ∑n=0∞-1n3n!n!n+1!n+2! we will use ratio test…

Q: 1 7. Determine by the ratio test if n- converges or diverges. п! -

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Q: 10. (x- 3)" Ln=1 n

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Q: 00 +8 dx converges. Perform a test to determine if - 00 x° +8 Does dx converge or diverge? .9 1…

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Q: 3 (k+ 3)! Evaluate Σ given that k=0 n=0 1 n! || e

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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: SntXn stx

A: We have to test the convergency.

Q: 26. The interval of convergence for (X-3)* k - (x– is а. (-3, 3] b. [-3, 3] с. (-2, 4) d. [2, 4] е.…

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Q: 5). Find the interval of convergence. ∞ n = 0 xn n7 + 8

A: Introduction: A power series can either be convergent everywhere or can be convergent over a…