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Let f:(1,3) → R be continuous on (1, 3). Then, for each & >0 and each u E (1,3) there exists a 0(E,u)> 0 such that |f(x)-f(u)] < ɛ whenever |x-u|

Let f:(1,3) → R be continuous on (1, 3). Then, for each & >0 and each u E (1,3) there exists a 0(E,u)> 0 such that |f(x)-f(u)] < ɛ whenever |x-u|

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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This material is Real analysis.
Let f:(1,3)→ R be continuous on (1, 3). Then, for each & >0 and each u E (1,3) there exists a 6(E,u)> 0 such that |f(x)-f(u)| < ɛ whenever |x-u| <d(ɛ,u). Let A = {0(E,u); ɛ E (0,0), u E (1,3)}. Which of the following sets A would guarantee that f is uniformly continuous on (1,3)? Select one: a. none of the listed sets guarantees the uniform continuity off over (1,3). Ob.A=(Tin(3-u) E E (0,00), u E (1,3)} In(3-u)| OcA=(e(3-u)E E (0, x), u E (1,3)} O d. A=( E E (0, ∞), u E (1,3)}
Transcribed Image Text:Let f:(1,3)→ R be continuous on (1, 3). Then, for each & >0 and each u E (1,3) there exists a 6(E,u)> 0 such that |f(x)-f(u)| < ɛ whenever |x-u| <d(ɛ,u). Let A = {0(E,u); ɛ E (0,0), u E (1,3)}. Which of the following sets A would guarantee that f is uniformly continuous on (1,3)? Select one: a. none of the listed sets guarantees the uniform continuity off over (1,3). Ob.A=(Tin(3-u) E E (0,00), u E (1,3)} In(3-u)| OcA=(e(3-u)E E (0, x), u E (1,3)} O d. A=( E E (0, ∞), u E (1,3)}
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