Results 1 to 3 of 3

Thread: Help: Case analysis

  1. #1
    Junior Member rednest's Avatar
    Joined
    Mar 2008
    Posts
    36

    Help: Case analysis

    Solve the inequality $\displaystyle \frac{1}{x}<x<1$ by Case Analysis.

    What is 'Case Analysis' ??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,743
    Thanks
    2814
    Awards
    1
    Consider two cases:
    Case I. $\displaystyle x>0$ and then solve.

    Case II. $\displaystyle x<0$ annd then sove.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    Have you noticed that on MA132 Foundations Exercises 1 there's a typo in Section A? 1 ii) doesn't make sense!

    Anyway, plato was right with what he posted.

    Remember to flip the inequality sign around when you take s as a negative.

    $\displaystyle \frac{1}{x}<x<1$

    If x is negative then multiply through by x and flip the signs around:

    $\displaystyle 1>x^2>x$

    Then solve each separate equation:

    $\displaystyle 1>x^2$ and $\displaystyle x^2>x$.

    When x is positive, just solve $\displaystyle 1<x^2<x$ by splitting it into two separate inequalities like above.

    Hope it helps!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ambiguous Case Help
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: Dec 4th 2011, 09:30 AM
  2. DE: The Case of Duplication
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: May 12th 2011, 07:34 AM
  3. I've never understood why this is the case
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: Feb 14th 2009, 05:53 AM
  4. Need Help with statistics case
    Posted in the Statistics Forum
    Replies: 5
    Last Post: Jan 29th 2009, 03:20 PM

Search Tags


/mathhelpforum @mathhelpforum