For the given function f(x) and values of L, c, and e > 0 find the largest open interval about c on which the inequality |f(x) – L| 0 such that 0 < |x - c| < 8 → |f(x) – L| < ɛ. c= 5, f(x) = V18x + 31, L= 11, e = 0.1

For the given function f(x) and values of L, c, and e > 0 find the largest open interval about c on which the inequality |f(x) – L| 0 such that 0 < |x - c| < 8 → |f(x) – L| < ɛ. c= 5, f(x) = V18x + 31, L= 11, e = 0.1

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 15BEXP

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Question

For the given function f(x) and values of L, c, and e > 0 find the largest open interval about c on which the inequality |f(x) – L| <e holds. Then determine the largest value
for 6 >0 such that 0 < |x - c| < 8 → |f(x) – L| < ɛ.
c= 5,
f(x) = V18x + 31,
L= 11,
e = 0.1

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It is given that,

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On further simplification,

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Find the largest value δ > 0 as follows. Now,

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