Question 10 Suppose (f) converges on a set DCR to f. Let (r,) be a sequence in D, that converges tor€ D. Is it true that lim f. (In) = f (x)?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Question 10**

Suppose \((f_n)\) converges on a set \(D \subseteq \mathbb{R}\) to \(f\). Let \((x_n)\) be a sequence in \(D\) that converges to \(x \in D\). Is it true that

\[ \lim_{n \to \infty} f_n(x_n) = f(x)? \]
Transcribed Image Text:**Question 10** Suppose \((f_n)\) converges on a set \(D \subseteq \mathbb{R}\) to \(f\). Let \((x_n)\) be a sequence in \(D\) that converges to \(x \in D\). Is it true that \[ \lim_{n \to \infty} f_n(x_n) = f(x)? \]
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