7. Suppose (fn) is a sequence of continuous functions on an interval I that converges uniformly on I to a function f. If (xn) C I converges to xo E I, show that lim,→∞ fn(xn) = f(xo).
7. Suppose (fn) is a sequence of continuous functions on an interval I that converges uniformly on I to a function f. If (xn) C I converges to xo E I, show that lim,→∞ fn(xn) = f(xo).
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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Transcribed Image Text:7. Suppose (fn) is a sequence of continuous functions on an interval I that
converges uniformly on I to a function f. If (xn) C I converges to xo E I,
show that lim, n(Xn) = f(xo).
n→∞
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