Let f E C(0, 1). Suppose that lim f(x) and lim f(x) exist (and are finite). Show that • f(x) is bounded in (0, 1);
Let f E C(0, 1). Suppose that lim f(x) and lim f(x) exist (and are finite). Show that • f(x) is bounded in (0, 1);
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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How do solve the first question? Thank you!
Transcribed Image Text:Let f E C(0, 1). Suppose that lim f(x) and lim f(x) exist (and are finite). Show that
• f(x) is bounded in (0, 1);
f(x) is uniformly continuous in (0,1). Hint: prove by contradiction.
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