Which of the following statements are equivalent? For all e > 0, there exists a ô > 0 such that |x – c| < 8 (and x E A) implies |f(x) – f(c)| < e V For all Ve f(c)), there exists a V;(c) such that x e V;(c) (and x E A) implies f(x) e Ve f(c)) V For all (xn) → c (with x, E A), it follows that f(xn) → f(c). limx»c f(x) = f(c)
Which of the following statements are equivalent? For all e > 0, there exists a ô > 0 such that |x – c| < 8 (and x E A) implies |f(x) – f(c)| < e V For all Ve f(c)), there exists a V;(c) such that x e V;(c) (and x E A) implies f(x) e Ve f(c)) V For all (xn) → c (with x, E A), it follows that f(xn) → f(c). limx»c f(x) = f(c)
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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Transcribed Image Text:Which of the following statements are equivalent?
For all e > 0, there exists a ô > 0 such that |x – c| < 8 (and x E A) implies |f(x) – f(c)| < e
For all Ve f(c)), there exists a V5(c) such that x E V¿(c) (and x E A) implies f(x) E Ve f(c))
For all (xn)
→ c (with x, E A), it follows that f(xn) → f(c).
limx»c f(x) = f (c)
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