Results 1 to 7 of 7

Math Help - Need help finding δ in this calculus problem!

  1. #1
    Junior Member
    Joined
    Feb 2013
    From
    PA
    Posts
    26

    Need help finding δ in this calculus problem!

    Hi all,

    The problem shows the graph of f(x) = x^2 - 1 and asks to find δ such that if 0 < |x - 2| < δ, then |f(x) - 3| < 0.2.

    This is in the first chapter of my calculus book and dealing strictly with limits but I don't know how to do the problem, anyone want to chime in?

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,956
    Thanks
    1780
    Awards
    1

    Re: Need help finding δ in this calculus problem!

    Quote Originally Posted by Odonsky View Post
    The problem shows the graph of f(x) = x^2 - 1 and asks to find δ such that
    if 0 < |x - 2| < δ, then |f(x) - 3| < 0.2.
    First take note that |f(x)-3|=|x-2|\;|x+2|. HOW & WHY?

    Note that the factor |x-2| is the one we control with the \delta~.

    Work your way through the following:
    \\|x-2|<1~\Rightarrow\\-1<x-2<1~\Rightarrow\\1<x<3~\Rightarrow\\3<x+2<5 \\|x+2|<5

    So the other factor |x+2| is less that five if we start with \delta<1.

    What would happen if \delta=\frac{1}{25}~?

    Well \delta<1 so |f(x)-3|=|x-2|\;|x+2|<\frac{1}{25}\cdot 5<~?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2013
    From
    PA
    Posts
    26

    Re: Need help finding δ in this calculus problem!

    Quote Originally Posted by Plato View Post
    First take note that |f(x)-3|=|x-2|\;|x+2|. HOW & WHY?

    Note that the factor |x-2| is the one we control with the \delta~.

    Work your way through the following:
    \\|x-2|<1~\Rightarrow\\-1<x-2<1~\Rightarrow\\1<x<3~\Rightarrow\\3<x+2<5 \\|x+2|<5

    So the other factor |x+2| is less that five if we start with \delta<1.

    What would happen if \delta=\frac{1}{25}~?

    Well \delta<1 so |f(x)-3|=|x-2|\;|x+2|<\frac{1}{25}\cdot 5<~?
    To answer the first question as to why |f(x) - 3| = |x - 2| |x + 2| I really do not know why, so the rest of it does not make sense either.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,956
    Thanks
    1780
    Awards
    1

    Re: Need help finding δ in this calculus problem!

    Quote Originally Posted by Odonsky View Post
    To answer the first question as to why |f(x) - 3| = |x - 2| |x + 2| I really do not know why, so the rest of it does not make sense either.
    If that is true, then you are clearly not prepared for a course in calculus.

    As a retired chair of a university mathematics department, I advise you to do a good course in Pre-Calculus.
    You need a good review of the properties of absolute value and inequalities. I suspect you could benefit in many more ways from such a course.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602

    Re: Need help finding δ in this calculus problem!

    Surely you can at least evaluate f(x) - 3 and factorise it...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2013
    From
    PA
    Posts
    26

    Re: Need help finding δ in this calculus problem!

    Quote Originally Posted by Plato View Post
    If that is true, then you are clearly not prepared for a course in calculus.

    As a retired chair of a university mathematics department, I advise you to do a good course in Pre-Calculus.
    You need a good review of the properties of absolute value and inequalities. I suspect you could benefit in many more ways from such a course.
    I am in the process of preparing for an upcoming summer calculus course and have never taken this subject before, hence my inability to solve the above problem set.
    I'm trying to self-study in the meantime using the internet.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Feb 2013
    From
    PA
    Posts
    26

    Re: Need help finding δ in this calculus problem!

    Quote Originally Posted by Prove It View Post
    Surely you can at least evaluate f(x) - 3 and factorise it...
    What I know about evaluating a function is to substitute x with whatever it equals but in this case I do not know what x equals.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: January 16th 2011, 07:45 AM
  2. Replies: 4
    Last Post: October 25th 2010, 07:18 PM
  3. Calculus Word Problem-Finding Max Profit
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 22nd 2009, 08:24 PM
  4. Replies: 4
    Last Post: February 19th 2009, 05:27 PM
  5. Replies: 1
    Last Post: November 2nd 2008, 06:28 PM

Search Tags


/mathhelpforum @mathhelpforum