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I have made some observations regarding the Precise Limit Definition.

For any given polynomial:

[tex]ax^n[/tex]

The solution for delta is:

[tex]\boxed{\delta = \frac{\epsilon^{\frac{1}{n}}}{|a|}}[/tex]

The solution for epsilon is:

[tex]\boxed{\epsilon = (|a| \delta)^n}[/tex]

My Calculus textbook determines the values for delta and epsilon experimentally based upon the primary numerator function, however these equations have worked for every problem that was assigned to me.

Are these solutions correct?

What are the possibilities that there is a theorem that may exist that determines the solutions for ALL deltas and epsilons?

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# Precise Limits

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