For all e>0 there exists d>0 such that |x-a|

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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Rewrite the following sentence mean with f(x) = 2x+3 and  a=2. 

 

"For all e>0 there exists d>0 such that |x-a|<d implies |f(x)-L|< e"

 

 

 

Graph the function f(x) = 2x+3 near a=2.

 

 

 

What will L need to be for this implication to maybe be true?

 

 

 

Draw and label lines on your graph to show how d and e relate to the graph.  Attach a picture of this (or a screenshot).

 

 

 

 

 

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