For the given function f(x) and numbers L, c, and ɛ >0, find an open interval about c on which the inequality f(x) – L <ɛ holds. Then give a value for 6>0 such that for all x satisfying0< |x-c| < & the inequality |f(x) –L| 0 such that for all x satisfying 0 < x - c <& the inequality f(x) – L < ɛ holds.8 =(Simplify your answer.)

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Answered: For what open interval does the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 80E

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Question

For the given function f(x) and numbers L, c, and ɛ >0, find an open interval about c on which the inequality f(x) – L <ɛ holds. Then give a value for 6>0 such that for all x satisfying
0< |x-c| < & the inequality |f(x) –L|<e holds.
f(x) = /29 - x, L=1, c = 28, ɛ = 1
%3D
.....
For what open interval does the inequality f(x) – L < ɛ hold?
(Simplify your answer. Type your answer in interval notation.)
Find the largest value &> 0 such that for all x satisfying 0 < x - c <& the inequality f(x) – L < ɛ holds.
8 =
(Simplify your answer.)

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For what open interval does the inequality |f(x) - L 0 such that for all x satisfying 0< |x- c| <8 the inequality |f(x) – L| < ɛ holds. 8 = (Simplify your answer.)