Use Graph to Find Delta...2

Discussion in 'Calculus' started by nycmathguy, May 7, 2022.

1. nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
422
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.

nycmathguy, May 7, 2022
2. MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,884
(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?

MathLover1, May 10, 2022
nycmathguy likes this.
3. nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
422
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"?

nycmathguy, May 11, 2022
4. MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,884
since , so you need 2,something means little bit more than 2 to have a limit
in your case I used 2.01

MathLover1, May 11, 2022
nycmathguy likes this.

Joined:
Jun 27, 2021
Messages:
5,386