8. Prove that lim(x_) = 0 if and only if lim(jx,i) = 0. Give an example to show that the conver- gence of (ix,i) need not imply the convergence of (x,).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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8. Prove that lim(x,) =0 if and only if lim()x,1) = 0. Give an example to show that the conver-
gence of (1x, 1) need not imply the convergence of (x,).
Transcribed Image Text:8. Prove that lim(x,) =0 if and only if lim()x,1) = 0. Give an example to show that the conver- gence of (1x, 1) need not imply the convergence of (x,).
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