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Let f: R R be a function. Select ALL of the following statements which are equivalent to the statement that f is continuous. a. Vc ER, VD > 0,38 > 0: x-cl < 8⇒ f(x)-f(c)| < D. b. VER, 3D > 0,38 > 0: c. 3cER, VE> 0,36 > 0: d. Vc E R, Ve > 0,36 > 0: x-cl < 8⇒ |f(x)-f(c)| < D. x-cl < 8⇒ [f(x) = f(c)| < e. x-cl < 6⇒ [f(x) = f(c)| < e.

Let f: R R be a function. Select ALL of the following statements which are equivalent to the statement that f is continuous. a. Vc ER, VD > 0,38 > 0: x-cl < 8⇒ f(x)-f(c)| < D. b. VER, 3D > 0,38 > 0: c. 3cER, VE> 0,36 > 0: d. Vc E R, Ve > 0,36 > 0: x-cl < 8⇒ |f(x)-f(c)| < D. x-cl < 8⇒ [f(x) = f(c)| < e. x-cl < 6⇒ [f(x) = f(c)| < e.

Advanced Engineering Mathematics
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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Let f: R→ R be a function. Select ALL of the following statements which are equivalent to the statement that f is continuous. a. VcR, VD > 0,38 > 0: x-cl < 8⇒ f(x)-f(c)| < D. b. VER, 3D > 0,38 > 0: x-cl < 8⇒ |f(x)-f(c)| < D. c. 3c R, Ve > 0,36 > 0: x-c| < 6 ⇒ [f(x) = f(c) < €. d. Vc E R, Ve > 0,36 > 0: x-cl < 6⇒ [f(x) = f(c)| < €.
Transcribed Image Text:Let f: R→ R be a function. Select ALL of the following statements which are equivalent to the statement that f is continuous. a. VcR, VD > 0,38 > 0: x-cl < 8⇒ f(x)-f(c)| < D. b. VER, 3D > 0,38 > 0: x-cl < 8⇒ |f(x)-f(c)| < D. c. 3c R, Ve > 0,36 > 0: x-c| < 6 ⇒ [f(x) = f(c) < €. d. Vc E R, Ve > 0,36 > 0: x-cl < 6⇒ [f(x) = f(c)| < €.
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