Ee whether or not fn converges uniformly nclusion. b) (0, 1)

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: S1, S2, 2. Show that if (fn)n converges uniformly on U- Sk. S,, then (fn)n converges uniformly on…

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

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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: 1 Prove that Σn=1 4² converges uniformly on R.

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Q: For each nЄ Z+ let fn : R → R be the function пх fn(2) n|x| +1° (a) Prove that (fn) converges…

A: Given the sequence of functions  defined by .(a)Consider the limit,This is true for every 0≠x∈R.…

Q: If |fn(x)| < an for all r and E=1 an converges, prove that En=1 fn(1) converges uniformly.

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Q: Help for 2a,2b,2c.

A: Given,

Q: s cos (31TK) m(k) ksi it aly converges condifione is or absoluety 人口

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Q: (c) Show that fn (x) : x2+n? converges uniformly on [0, 0).

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

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Q: Suppose (xn) does not converge to 0. Then there exists e>0 such that all except for finitely many…

A: Consider the sequence xn=1,0,1,0,1,0,....... Here the odd terms are 1 and the even terms are 0.…

Q: 9. Prove that if {fn(x)} converges uniformly to the function f(x) on each of the sets A1, A2, ...,…

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Q: Exercise 4. 1. Show that if (fn)n converges uniformly on S, then (fn)n converges uniformly on every…

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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: Suppose {fn}n=1 converges uniformly on E. Show {fn}n=1 converges pointwise on E.

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