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Math Help - Definition of Limit

  1. #1
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    Definition of Limit

    There's a similar post on this, but I can't understand it and it seems flawed. So I'll try this one.
    How do you prove that the lim (as x approaches a) of x^2=a^2?
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  2. #2
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    Are you familiar with the delta-epsilon defintion of a limit? I don't want to go into it if it's not what you're looking for.
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  3. #3
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    Yes I am.
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  4. #4
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    Here's a good site that proves \lim_{x \to 1}x^2+3=4 It uses the same method so unless you want I won't type it all out.

    http://www.math.ucdavis.edu/~kouba/C...l#SOLUTION%204
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  5. #5
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    Thank you. Very helpful.
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  6. #6
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    Ok. So the only thing I don't get now as how it works for something like the example I had where the limit equals a variable (also the number the limit is approaching is a variable). I'm having trouble making the connection from the problem I had to ones with real numbers.

    How do you show abs(x^2-a^2) is less than epsilon?
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