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)| < €.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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Please follow the steps and show all the required parts in the question. Thanks
![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)| < €.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2F7d59c216-e895-4f4e-8d0f-917b6dae6290%2Fa2kuid5_processed.png&w=3840&q=75)
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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