Let fn(x) on [0, 1]. 1+ x" (a) Prove that fn converges uniformly to 0 on [0, €], Ve E (0, 1). (b) Does fn converge uniformly on [0, 1]? Prove or disprove.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let fn(x) :
on [0, 1].
1+ x"
(a) Prove that fn converges uniformly to 0 on [0, e], Ve E (0, 1).
(b) Does fn converge uniformly on [0, 1]? Prove or disprove.
x sin nx
Let fn(x) = x +
on R.
n
(a) Prove that fn converges uniformly to x on [-R, R], VR > 0.
(b) Does fn converge uniformly on R? Prove or disprove.
Transcribed Image Text:Let fn(x) : on [0, 1]. 1+ x" (a) Prove that fn converges uniformly to 0 on [0, e], Ve E (0, 1). (b) Does fn converge uniformly on [0, 1]? Prove or disprove. x sin nx Let fn(x) = x + on R. n (a) Prove that fn converges uniformly to x on [-R, R], VR > 0. (b) Does fn converge uniformly on R? Prove or disprove.
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