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Suppose that fn(x) and f(x) are functions R –→ R. Suppose also that fn converges uniformly to f as n → 0. Does the function fn(x)² converge uniformly to f(x)²? Either prove that it does, or find a counterexample.

Suppose that fn(x) and f(x) are functions R –→ R. Suppose also that fn converges uniformly to f as n → 0. Does the function fn(x)² converge uniformly to f(x)²? Either prove that it does, or find a counterexample.

Advanced Engineering Mathematics
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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Suppose that fn(x) and f(x ) are functions R → R. Suppose also that fn converges uniformly to f as n → 0. Does the function f,(x) converge uniformly to f(x)?? Either prove that it does, or find a counterexample.
Transcribed Image Text:Suppose that fn(x) and f(x ) are functions R → R. Suppose also that fn converges uniformly to f as n → 0. Does the function f,(x) converge uniformly to f(x)?? Either prove that it does, or find a counterexample.
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