Suppose f: R → R is a function, and f(0) = 0. Which one of the following statements is equivalent to saying that f is discontinuous at 0? (3 > 0) (V6 > 0) (3x € R)(\r] < 8 ⇒ [ƒ(x)| ≥ ɛ) O (VE > 0) (360)(Vx ≤ R)([x] ≥ 8 ⇒ |ƒ(x)| ≥ ɛ) (3 > 0) (V8 > 0) (3x € R) (|x| < 8 and [f(x)| > €) (3€ > 0) (V6 > 0) (3x € R)(|x| ≥ 6 and [f(x)| ≥ €) (€ > 0) (0) (3x € R) (|r| ≥ 6 ⇒ |ƒ(x)| ≥ ɛ)
Suppose f: R → R is a function, and f(0) = 0. Which one of the following statements is equivalent to saying that f is discontinuous at 0? (3 > 0) (V6 > 0) (3x € R)(\r] < 8 ⇒ [ƒ(x)| ≥ ɛ) O (VE > 0) (360)(Vx ≤ R)([x] ≥ 8 ⇒ |ƒ(x)| ≥ ɛ) (3 > 0) (V8 > 0) (3x € R) (|x| < 8 and [f(x)| > €) (3€ > 0) (V6 > 0) (3x € R)(|x| ≥ 6 and [f(x)| ≥ €) (€ > 0) (0) (3x € R) (|r| ≥ 6 ⇒ |ƒ(x)| ≥ ɛ)
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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![Suppose f: R → R is a function, and f(0) = 0. Which one of the
following statements is equivalent to saying that f is discontinuous at 0 ?
(3€ > 0) (0) (3x € R) ([x] < 8⇒ |f(x) > €)
O (VE > 0) (38 > 0) (Vx ≤ R) (|x| ≥ 8 ⇒ |f(x)| ≥ ɛ)
(30)(180) (3x € R) (|x| < 8 and f(x) > €)
(€ > 0) (0) (3x = R) (x ≥ 8 and f(x) > €)
(3€ > 0) (0) (3x € R) ([x] ≥ 8 ⇒ |f(x)| ≥ ɛ)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d370c3-9e4b-442d-9a89-d591c5ced338%2Ffed7d3c8-e2e7-47be-bb52-0d3a224d21fd%2F1hp25od_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose f: R → R is a function, and f(0) = 0. Which one of the
following statements is equivalent to saying that f is discontinuous at 0 ?
(3€ > 0) (0) (3x € R) ([x] < 8⇒ |f(x) > €)
O (VE > 0) (38 > 0) (Vx ≤ R) (|x| ≥ 8 ⇒ |f(x)| ≥ ɛ)
(30)(180) (3x € R) (|x| < 8 and f(x) > €)
(€ > 0) (0) (3x = R) (x ≥ 8 and f(x) > €)
(3€ > 0) (0) (3x € R) ([x] ≥ 8 ⇒ |f(x)| ≥ ɛ)
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