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3. a) b) For the sequence of functions Find its pointwise limit fn (2) for x = [0, 1]. Justify your answer = Theorem nx² + 2x n x = [0, 1]. f (x) = lim fn(x) n→∞ Show that fnf uniformly on [0, 1]. Justify your answer State the theorem from class which allows to find limn→∞ f¹ fn (x) dx by computing f f (x) dx

3. a) b) For the sequence of functions Find its pointwise limit fn (2) for x = [0, 1]. Justify your answer = Theorem nx² + 2x n x = [0, 1]. f (x) = lim fn(x) n→∞ Show that fnf uniformly on [0, 1]. Justify your answer State the theorem from class which allows to find limn→∞ f¹ fn (x) dx by computing f f (x) dx

Advanced Engineering Mathematics
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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3. a) b) d) For the sequence of functions Find its pointwise limit fn (2) for x = [0, 1]. Justify your answer nx² + 2x Theorem n x = [0, 1]. f (x) = lim fn(x) n→∞ Show that fnf uniformly on [0, 1]. Justify your answer State the theorem from class which allows to find limn→∞ f fn (x) dx by computing f f (x) dx Verify the assumptions of the theorem from part 4c) and compute limn→∞ fofn (x) dx using the theorem.
Transcribed Image Text:3. a) b) d) For the sequence of functions Find its pointwise limit fn (2) for x = [0, 1]. Justify your answer nx² + 2x Theorem n x = [0, 1]. f (x) = lim fn(x) n→∞ Show that fnf uniformly on [0, 1]. Justify your answer State the theorem from class which allows to find limn→∞ f fn (x) dx by computing f f (x) dx Verify the assumptions of the theorem from part 4c) and compute limn→∞ fofn (x) dx using the theorem.
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