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**[SOLVED] Epsilon Delta Proof**

Does this limit proof make total sense? Given : "Show that [tex]\lim_{x \rightarrow 2} x^{2} = 4[/tex]."

My attempt at it :[tex]0<|x^{2}-4|<\epsilon[/tex] which can also be written as [tex]0<|(x-2)(x+2)|<\epsilon[/tex].

[tex]0<|x-2|<\delta[/tex] where [tex]\delta > 0[/tex]. It appears that [tex]\delta = \frac {\epsilon}{x+2}[/tex] which is the conversion factor. Which then by substitution, [tex]0<|x-2|<\frac {\epsilon}{x+2}[/tex].

Here is the actual proof:

Choose [tex]\delta = \frac {\epsilon}{x+2}[/tex], given [tex]epsilon > 0[/tex] then if [tex]0<|x-2|<\frac {\epsilon}{x+2}[/tex] then [tex]0<|(x-2)(x+2)|<\delta[/tex].

Is this explanation coherent? I actually have a slight idea of what I wrote. Hopefully I am on the right path.

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