Delta-Epsilon Definition of a Limit...7

[nycmathguy]

Calculus
Section 1.7

How about 32?

 

[MathLover1]

32.

For ε>0 you would take δ< min{ε/19,1} because then |x−2|<δ implies:

|x^3−8| ≤δ (δ^2+6δ+12) < (ε/19)(1+6+12)=ε

so,

 

[nycmathguy]

32.
View attachment 2735

For ε>0 you would take δ< min{ε/19,1} because then |x−2|<δ implies:

|x^3−8| ≤δ (δ^2+6δ+12) < (ε/19)(1+6+12)=ε

so, View attachment 2736

I hope to someday make sense of this material. I think Jenn covers this section in her curriculum. It is great to understand this stuff but certainly not needed to do calculus.