3. Prove that the function f: [∞) → R; f(x) = 1 is uniformly contin- uous.
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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Question
Solve using a theorem or definition for uniform continuity.
![definition (p. 83).
3. Prove that the function f: [,∞) → R; f(x) = ½ is uniformly contin-
uous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febf30032-6a45-43dc-84f6-3d2dba8b9144%2F4916baa3-50cf-4bee-a95d-5b180817febc%2F4j70cyy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:definition (p. 83).
3. Prove that the function f: [,∞) → R; f(x) = ½ is uniformly contin-
uous.
![DEFINITION A function f:D → R is uniformly continuous on E C D iff
for every > 0, there is 8 > 0 such that if x, y € E with x - y)< 8, then
f(x) = f(y)<e. If f is uniformly continuous on D, we say f is uniformly
continuous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febf30032-6a45-43dc-84f6-3d2dba8b9144%2F4916baa3-50cf-4bee-a95d-5b180817febc%2Fqhqg535_processed.jpeg&w=3840&q=75)
Transcribed Image Text:DEFINITION A function f:D → R is uniformly continuous on E C D iff
for every > 0, there is 8 > 0 such that if x, y € E with x - y)< 8, then
f(x) = f(y)<e. If f is uniformly continuous on D, we say f is uniformly
continuous.
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