3. Define fn on (0, 1) by fn(x) = x". Show that fn converges to the constant function 0, but that this convergence is not uniform.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**3. Problem Statement:**

Define the sequence of functions \( f_n \) on the interval (0, 1) by

\[
f_n(x) = x^n.
\]

**Question:**

Show that \( f_n \) converges to the constant function 0, but that this convergence is *not* uniform.
Transcribed Image Text:**3. Problem Statement:** Define the sequence of functions \( f_n \) on the interval (0, 1) by \[ f_n(x) = x^n. \] **Question:** Show that \( f_n \) converges to the constant function 0, but that this convergence is *not* uniform.
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