: 1. Let f RR be a function and let c E R. Prove that lim f(x) exists if and only if for every ε > 0, there exists a > 0 such that x c |f(x) − f(y) < E for x, y Є R satisfying 0 < |x − c| < ♂ and 0 < |y − c| < d.

: 1. Let f RR be a function and let c E R. Prove that lim f(x) exists if and only if for every ε > 0, there exists a > 0 such that x c |f(x) − f(y) < E for x, y Є R satisfying 0 < |x − c| < ♂ and 0 < |y − c| < d.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 23E

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please answer quesiton with full steps showing all detail

:
1. Let f RR be a function and let c E R. Prove that lim f(x) exists if and only if for every ε > 0, there
exists a > 0 such that
x c
|f(x) − f(y) < E
for x, y Є R satisfying 0 < |x − c| < ♂ and 0 < |y − c| < d.

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