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Description: 1.1 Let {fn(x)} = {x ER and x > 0.1+ xn1.1.1 Find the pointwise limit of the sequence {fn(x)} if it exists.1.1.2 Show that if 0

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1.1 Let {fn(x)} = { ,x ER and r > 0. %3D + xn 1.1.1 Find the pointwise limit of the sequence {fn(x)} if it exists. 1.1.2 Show that if 0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

1.1 Let {fn(x)} = {
x ER and x > 0.
1+ xn
1.1.1 Find the pointwise limit of the sequence {fn(x)} if it exists.
1.1.2 Show that if 0 <t < 1, the sequence {fn(x)} converges uniformly on [0, t|.
1.1.3 Show that the convergence is not uniform on [0, 1].

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1.1