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Problem 3 Medium Difficulty

Formal Definition of Limit Given the limit

$\lim _{x \rightarrow 2}(2 x+1)=5$
use a sketch to show the meaning of the phrase
$$" 0<|x-2|<0.25$ implies $|(2 x+1)-5|<0.5"$$

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Video Transcript

you're given a falling limit as X approaches to of two X plus one is equal to five and you are to create a sketch of a graph to show that zero is less than absolute volley of maximized to is Austin 0.25 It implies the absolute value two X plus one minus five is awesome. But so we can just simply go and grab this. So, looking at a graph, this is we have our line. So the red line is two X plus one and you can see that as we got, but of the absolute values, you can see that they encompass the same exact section. So even though one because the slope is to act. So even though one of the, um one of the phrases is from 0 to 0.25 years from 0 to 0.5, you can see that they still they still are equal to each other because they accompany the same section