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Check if the sequence is uniformly convergent using the steps listed below: n+sin(nx) b. fn (x) = " XER Hint: Please consider the following steps: • Fix x ER and show that • Define f: R→ R, lim_ƒn (x) = 1. n→∞ ƒ (x) = 1. • Make your conclusion about pointwise convergence of {fn (x)}. • Fix n E N and show that, for all x € R, |fn (x) - f (x)| ≤ 3 8n + 4 • Fix € > 0 and show that, there is NE N, such that for all n > N and for all x ER, |fn (x) = f (x)| < €.

Check if the sequence is uniformly convergent using the steps listed below: n+sin(nx) b. fn (x) = " XER Hint: Please consider the following steps: • Fix x ER and show that • Define f: R→ R, lim_ƒn (x) = 1. n→∞ ƒ (x) = 1. • Make your conclusion about pointwise convergence of {fn (x)}. • Fix n E N and show that, for all x € R, |fn (x) - f (x)| ≤ 3 8n + 4 • Fix € > 0 and show that, there is NE N, such that for all n > N and for all x ER, |fn (x) = f (x)| < €.

Algebra & Trigonometry with Analytic Geometry
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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Check if the sequence is uniformly convergent using the steps listed below: n+sin(nx) b. fn (x) = " XER Hint: Please consider the following steps: • Fix x ER and show that • Define f : R → R, lim_fn (x) = 1. n→∞ ƒ (x) = 1. • Make your conclusion about pointwise convergence of {fn (x)}. • Fix n E N and show that, for all x € R, |fn (x) - f (x)| ≤ 3 8n + 4 • Fix € > 0 and show that, there is NE N, such that for all n > N and for all x ER, |fn (x) = f(x)| < €.
Transcribed Image Text:Check if the sequence is uniformly convergent using the steps listed below: n+sin(nx) b. fn (x) = " XER Hint: Please consider the following steps: • Fix x ER and show that • Define f : R → R, lim_fn (x) = 1. n→∞ ƒ (x) = 1. • Make your conclusion about pointwise convergence of {fn (x)}. • Fix n E N and show that, for all x € R, |fn (x) - f (x)| ≤ 3 8n + 4 • Fix € > 0 and show that, there is NE N, such that for all n > N and for all x ER, |fn (x) = f(x)| < €.
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