Results 1 to 3 of 3

Math Help - Basic inequality

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    42

    Basic inequality

    Cannot solve this for the life of me...

    When is 2t / (t+1)^3 > 0 ?
    I seem to think it is (-infinity,-1)U[0,infinity), but then I am unsure.

    The above expression is also equivelant to 2 / (t^2 (1 + 1/t)^3) - and that is only positive for t > -1.
    I am extremely confused!! Help!!! Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,905
    Thanks
    765
    Hello, Volcanicrain!

    When is: . \frac{2t}{(t+1)^3} \:>\: 0

    I seem to think it is: . (\text{-}\,\infty, \text{-}1) \cup (0,\infty) . . . . Right!


    The above expression is also equivelant to: . \frac{2}{t^2\left(1 + \frac{1}{t}\right)^3} \:>\:0 . . . . I agree
    . . and that is only positive for t > -1 . . . . no
    We have: . \frac{2t}{(t+1)^3} \;>\;0

    A fraction is positive if the numerator and denonominator are: . \begin{Bmatrix}(1) & \text{ both positive} \\ (2) & \text{ both negative} \end{Bmatrix}


    (1) Both positive: . \begin{Bmatrix}<br />
2t \:>\:0 & \Rightarrow & t \:>\:0 \\<br />
(t+1)^3 \:>\:0 & \Rightarrow & t+1 \:>\:0 & \Rightarrow & t \:>\:\text{-}1 \end{Bmatrix} \quad\Rightarrow\quad t \:>\:0

    (2) Both negative: . \begin{Bmatrix}<br />
2t \:<\:0 & \Rightarrow & t \:<\:0 \\<br />
(t+1)^3 \:<\:0 & \Rightarrow & t+1 \:<\:0 & \Rightarrow & t \:<\:\text{-}1 \end{Bmatrix} \quad\Rightarrow\quad t \:<\:\text{-}1


    Therefore: . (t \,<\,\text{-}1) \vee (t \,>\,0) \quad\Longleftrightarrow\quad (\text{-}\,\infty, \text{-}\,1) \cup (0, \infty)


    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2008
    Posts
    42
    Could you explain why it's not positive only for t > -1 in my quote though?? I've thought about it all day and I can't understand why my algebra is wrong.

    Thank you for confirming my above work though! I am quite grateful!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Basic inequality proof
    Posted in the Algebra Forum
    Replies: 3
    Last Post: July 17th 2010, 04:25 PM
  2. Basic Inequality questions
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: June 30th 2009, 12:24 PM
  3. Basic inequality problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 19th 2009, 03:18 PM
  4. Basic Inequality question.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 19th 2009, 04:19 AM
  5. Basic Inequality
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 4th 2008, 11:12 AM

Search Tags


/mathhelpforum @mathhelpforum