For any integer n ≥ 1 and any x ∈ (0,∞), define fn(x)= nx/(1+nx) (a) Let a > 0 be given. Prove that {fn} converges uniformly on the interval (a, ∞). (b) Prove that {fn} does not converge uniformly on (0,∞).

For any integer n ≥ 1 and any x ∈ (0,∞), define fn(x)= nx/(1+nx) (a) Let a > 0 be given. Prove that {fn} converges uniformly on the interval (a, ∞). (b) Prove that {fn} does not converge uniformly on (0,∞).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 74E

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Question

For any integer n ≥ 1 and any x ∈ (0,∞), define fn(x)= nx/(1+nx)

(a) Let a > 0 be given. Prove that {fn} converges uniformly on the interval (a, ∞).

(b) Prove that {fn} does not converge uniformly on (0,∞).

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