[a, b] and let (fn) be a sequence of functions on I → R that converges on I to f. Suppose that each derivative f is continuous on I and that the sequence (fm) is uniformly convergent to g on I. Prove that 4. Let I f(x) – f(a) = | g(t) dt and that f'(x) = g(x) for all x E I.
[a, b] and let (fn) be a sequence of functions on I → R that converges on I to f. Suppose that each derivative f is continuous on I and that the sequence (fm) is uniformly convergent to g on I. Prove that 4. Let I f(x) – f(a) = | g(t) dt and that f'(x) = g(x) for all x E I.
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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![4. Let I
converges on I to f. Suppose that each derivative f, is continuous on I and
that the sequence (fm) is uniformly convergent to g on I. Prove that
[a, b] and let (fn) be a sequence of functions on I → R that
f(x) – f(a) = | g(t)dt
and that f'(x) = g(x) for all x E I.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d456ce1-cbfb-470f-8ef9-05bd7d57f044%2Ff08dfebc-130c-46dc-a479-98c00beef108%2Fkb8b4fm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Let I
converges on I to f. Suppose that each derivative f, is continuous on I and
that the sequence (fm) is uniformly convergent to g on I. Prove that
[a, b] and let (fn) be a sequence of functions on I → R that
f(x) – f(a) = | g(t)dt
and that f'(x) = g(x) for all x E I.
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