In(x) (a) Show (gn) converges uniformly on [0, 1] and find g = lim gn. Show that g is differentiable and compute g'(x) for all a e [0, 1]. (b) Now, show that (g) converges on [0, 1]. Is the convergence uniform? Set h = lim g, and compare h and g'. Are they the same?
In(x) (a) Show (gn) converges uniformly on [0, 1] and find g = lim gn. Show that g is differentiable and compute g'(x) for all a e [0, 1]. (b) Now, show that (g) converges on [0, 1]. Is the convergence uniform? Set h = lim g, and compare h and g'. Are they the same?
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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Exercise 6.3.1. Consider the sequence of functions defined by
![In(x)
(a) Show (gn) converges uniformly on [0, 1] and find g = lim gn. Show that g
is differentiable and compute g'(x) for all a e [0, 1].
(b) Now, show that (g) converges on [0, 1]. Is the convergence uniform? Set
h = lim g, and compare h and g'. Are they the same?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed2ab6cf-816b-4f2e-96c8-0e26e1b7b158%2F2281082d-46ea-41ee-8bfc-b74d178d827b%2Fx8cjwyu.png&w=3840&q=75)
Transcribed Image Text:In(x)
(a) Show (gn) converges uniformly on [0, 1] and find g = lim gn. Show that g
is differentiable and compute g'(x) for all a e [0, 1].
(b) Now, show that (g) converges on [0, 1]. Is the convergence uniform? Set
h = lim g, and compare h and g'. Are they the same?
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