Results 1 to 4 of 4

Math Help - Limits with inequalities

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    162

    Limits with inequalities

    Hi, I am just wondering if I have the correct understanding of the questions below (in image)



    For question 1. I got the highest value of the function is 19. I got this by subbing in 7.5 because the |x - 7| < 0.5 because it is looking 0.5 units within x=7. So the highest value has to be when it is either 6.5 or 7.5. It turns out f(7.5) = 19 was the highest value. Therefore, the answer is 19 correct? I am wondering because it does not include 7.5, therefore the highest value of the function has to be the limit of f(x) as x approaches 7.5, which is 19.


    For question two. The 0.3 units of 22. The 22 is the y-value of the function correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: Limits with inequalities

    Quote Originally Posted by Barthayn View Post
    Hi, I am just wondering if I have the correct understanding of the questions below (in image)
    For question 1. I got the highest value of the function is 19. I got this by subbing in 7.5 because the |x - 7| < 0.5 because it is looking 0.5 units within x=7. So the highest value has to be when it is either 6.5 or 7.5. It turns out f(7.5) = 19 was the highest value. Therefore, the answer is 19 correct?
    If |x-7|<0.5 that means x\in(6.5,7.5).
    Now on an open interval \left| {\frac{{x + 2}}{{x - 8}}} \right| cannot have a maximum.
    BUT you are right 19 is a upper bound.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    162

    Re: Limits with inequalities

    Just as I was thinking over a few minutes ago. So the lower bound is 17/3 while the upper bound is 19. The highest value between these is no value at all because you can always get closer to 16 while not touching 16. Thanks for aid.

    With question 2 though. The y-value (the limit) is 22 correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: Limits with inequalities

    Quote Originally Posted by Barthayn View Post
    With question 2 though. The y-value (the limit) is 22 correct?
    For the second one we want
    |(5x+2)-22|=|5x-20|<0.3.
    Factor out the 5 to get |x-4|<0.06.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using limits to find other limits
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 18th 2009, 05:34 PM
  2. Replies: 8
    Last Post: July 16th 2009, 03:45 PM
  3. Function limits and sequence limits
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 26th 2009, 01:45 PM
  4. [SOLVED] [SOLVED] Limits. LIMITS!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 25th 2008, 10:41 PM
  5. Inequalities
    Posted in the Algebra Forum
    Replies: 8
    Last Post: July 6th 2007, 12:29 PM

Search Tags


/mathhelpforum @mathhelpforum