Use Graph to Find Delta...2

[nycmathguy]

Calculus
Section 2.4

Can you work out 9 as a guide for me to do a few more on my own? Jenn does not teach how to do this in her video lessons.

 

[MathLover1]

(a) Use a graph to find a number such that if 2< delta < 2+delta then 1/(ln(x-1))>100

as you can see from the graph, at x=2 to x=2.something goes to infinity

so, 2+delta > 2
let 2.something be 2.01

2+delta=2.01 ->delta=0.01


(b) What limit does part (a) suggest is true?

 

[nycmathguy]

(a) Use a graph to find a number such that if 2< delta < 2+delta then 1/(ln(x-1))>100
View attachment 3037

as you can see from the graph, at x=2 to x=2.something goes to infinity

so, 2+delta > 2
let 2.something be 2.01

2+delta=2.01 ->delta=0.01


(b) What limit does part (a) suggest is true?

View attachment 3038

You said the following:

"as you can see from the graph, at x=2 to x=2.something goes to infinity"

What do you mean by "x = 2 to x = 2"?

 

[MathLover1]

since

, so you need 2,something means little bit more than 2 to have a limit
in your case I used 2.01

 

[nycmathguy]

since View attachment 3042, so you need 2,something means little bit more than 2 to have a limit
in your case I used 2.01

Thanks. BTW, we are almost done with the Epsilon-delta definition of a limit. I will not dwell too long in this section.