3. Prove that the function f: [∞) → R; f(x) = 1 is uniformly contin- uous.

Advanced Engineering Mathematics
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ISBN:9780470458365
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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.
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.
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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