Delta-Epsilon Definition of a Limit...8

[nycmathguy]

Calculus
Section 1.7

Let's end this section with a big bang. How about 24 and 26? Remember: No need to rush through any question. Next weekend we end with Chapter 1. Section 1.8 is all about Continuity. Hopefully, I will do better in terms of continuity. Thank you again for your help and patience. Enjoy your Sunday.

 

[MathLover1]

I already did 24

26.

proof:

Given ε > 0 take δ = ε^(1/3) > 0
if 0 < |x − 0| < δ = ε^(1/3)
then |x^3 − 0| = |x|^3 < δ^3 = ε

 

[nycmathguy]

I already did 24

26.
View attachment 2728

proof:

Given ε > 0 take δ = ε^(1/3) > 0
if 0 < |x − 0| < δ = ε^(1/3)
then |x^3 − 0| = |x|^3 < δ^3 = ε

Absolutely this is over my head. I will keep this as study notes should I ever decide to slowly and patiently try to male sense of it all.

 

[MathLover1]

I told you to avoid it until ready for it

 

[nycmathguy]

I told you to avoid it until ready for it

You are right. I told you that I wanted your notes to keep as future study notes.