We are trying to prove the following limit.lim (6 - 2x)x→6= -2Once we have specified in terms of &, one of the steps in the proof is toshow the following:If 0 < |□| < 8, then ||< &.Fill in the blanks (shown as square boxes) for this statement.

Given, To fill in the blanks for the following statement i.e.

Answered: We are trying to prove the following…

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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Question

We are trying to prove the following limit.
lim (6 - 2x)
x→6
= -2
Once we have specified in terms of &, one of the steps in the proof is to
show the following:
If 0 < |□| < 8, then ||< &.
Fill in the blanks (shown as square boxes) for this statement.

Expert Solution

Step 1: Given Information:

Given,

$limit as x rightwards arrow 6 of left parenthesis 6 minus 2 x right parenthesis equals negative 6 space bold left parenthesis bold space bold italic n bold italic o bold italic t bold space bold minus bold 2 bold right parenthesis.$

To fill in the blanks for the following statement i.e.

$i f space 0 less than open vertical bar left square bracket space right square bracket close vertical bar less than delta comma space t h e n space open vertical bar left square bracket space right square bracket close vertical bar less than epsilon.$