Formal Epsilon-Delta Definition of a Limit
- Dr. Jack L. Jackson II
Formal Epsilon-Delta Definiton of a Limit of a Function as x Approaches a Constant
What are the coordinates of the center of the purple box?
What are the height and width of the purple box?
What is the significance of the purple box? For a particular value of epsilon, how do we adjust delta so that the inequalities in the definition of the limit are satisfied?
For a particular value of epsilon, how can we see the largest corresponding value of delta so that the inequalities in the definition are satisfied?
What do we need to do if a smaller value of epsilon is chosen?
How can we tell from this exploration that the function has the limit that we specified?
How do we modify the definition and illustration for a right limit?
How do we modify the definition and illustration for a Left Limit?