Use Graph to Find Delta...2

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

  1. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    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.

    Screenshot_20220507-174108_Samsung Notes.jpg
     
    nycmathguy, May 7, 2022
    #1
  2. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    (a) Use a graph to find a number such that if 2< delta < 2+delta then 1/(ln(x-1))>100
    upload_2022-5-9_21-17-27.png

    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?

    upload_2022-5-9_21-20-15.gif
     
    MathLover1, May 10, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    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
    #3
  4. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    since upload_2022-5-10_18-40-2.gif , 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
    #4
    nycmathguy likes this.
  5. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Thanks. BTW, we are almost done with the Epsilon-delta definition of a limit. I will not dwell too long in this section.
     
    nycmathguy, May 11, 2022
    #5
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.