Exercise 6.1.11: Fix a continuous h: [a,b] → R. Let f (x) := h(x) for x = [a,b], f(x) := h(a) for x < a and f(x) = h(b) for all x > b. First show that f: R →R is continuous. Now let fn be the function g from Exercise 5.3.7 with e = 1/n, defined on the interval [a,b]. That is, • x+1/n n fn(x): = 2 Show that {f} converges uniformly to h on [a, b]. n=1
Exercise 6.1.11: Fix a continuous h: [a,b] → R. Let f (x) := h(x) for x = [a,b], f(x) := h(a) for x < a and f(x) = h(b) for all x > b. First show that f: R →R is continuous. Now let fn be the function g from Exercise 5.3.7 with e = 1/n, defined on the interval [a,b]. That is, • x+1/n n fn(x): = 2 Show that {f} converges uniformly to h on [a, b]. n=1
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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please answer the question in the image. show all work and explain all steps.
![Exercise 6.1.11: Fix a continuous h: [a,b] → R. Let f (x) := h(x) for x = [a,b], f(x) := h(a) for x < a
and f(x) = h(b) for all x > b. First show that f: R →R is continuous. Now let fn be the function g from
Exercise 5.3.7 with e = 1/n, defined on the interval [a,b]. That is,
• x+1/n
n
fn(x):
=
2
Show that {f} converges uniformly to h on [a, b].
n=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a49b22d-c2e7-40c7-ba9f-f03570a2f6b8%2Fc585f323-5e9b-4fcd-a1bf-e2dfbb9e188b%2Fvkvlyqd_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 6.1.11: Fix a continuous h: [a,b] → R. Let f (x) := h(x) for x = [a,b], f(x) := h(a) for x < a
and f(x) = h(b) for all x > b. First show that f: R →R is continuous. Now let fn be the function g from
Exercise 5.3.7 with e = 1/n, defined on the interval [a,b]. That is,
• x+1/n
n
fn(x):
=
2
Show that {f} converges uniformly to h on [a, b].
n=1
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