Finding the limit of a function as x approaches a.

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  • #1
S-z
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For the function, f(x)=x^2 I need to find the limit as x approaches a. I am sure the limit is a^2, but how can I prove this, should I use the epsilon delta method? if so, am I to set delta to [tex]\sqrt{}epsilon[/tex]?
thanks
 

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  • #2
CompuChip
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Why don't you try it.

Let [itex]\epsilon > 0[/itex] and set [itex]\delta = \sqrt{\epsilon}[/itex].
If [itex]|x - a| < \delta[/itex] then
[tex]|f(x) - a^2| = |x^2 - a^2| = \cdots \le \cdots \stackrel{?}{\le} \epsilon[/tex]
 

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