Understanding Epsilon Delta Limits Relationship in Calculus

[Miike012]

Homework Statement

Is my understanding correct?

As delta(y) and delta(x) approach X from points to the left and points to the right of X (x is what we wish to find the derivative of) then the x and y values of points to the left and right approach the x and y values of X.
And as the approach... delta x and delta y approach zero thus... the delta and epsilon shrink and shrink around X.

hope that isn't confusing.

Homework Equations

The Attempt at a Solution

 

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There is a lot of abitrary phrasing in your explanation; the same sort of phrasing that makes the typical definitions in calculus non-rigorous.

Try putting it into more solid terms and state clearly the relationship between delta and epsilon.