Results 1 to 3 of 3

Math Help - infinite limit

  1. #1
    DBA
    DBA is offline
    Member
    Joined
    May 2009
    Posts
    129

    infinite limit

    Hello,
    I do not understand this...

    Determine the infinite limit:

    lim x-->-3+ f(x); f(x) = x+2/x+3

    I looked at the numerator and denominator...

    (x+2) approaches -1 as x gets closer to -3 from the right and
    (x+3) approchaes 0 as x gets closer to -3 from the right

    How do I know that the function f(x) has an limit of negative infinity?
    How do I know that the limit is infinite at all? (Why not just "does not exist")

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by DBA View Post
    Hello,
    I do not understand this...

    Determine the infinite limit:

    lim x-->-3+ f(x); f(x) = x+2/x+3

    I looked at the numerator and denominator...

    (x+2) approaches -1 as x gets closer to -3 from the right and
    (x+3) approchaes 0 as x gets closer to -3 from the right

    How do I know that the function f(x) has an limit of negative infinity?
    How do I know that the limit is infinite at all? (Why not just "does not exist")

    Thanks
    You have \lim_{x \rightarrow -3^+} \frac{x+2}{x+3}.

    \frac{x+2}{x+3} = 1 - \frac{1}{x + 3} and it should be clear from a graph of y = 1 - \frac{1}{x+3} that \lim_{x \rightarrow -3^+} \left( 1 - \frac{1}{x+3} \right) = - \infty.

    This is different from \lim_{x \rightarrow -3} \left( 1 - \frac{1}{x+3} \right), which does not exist because the left hand limit is not equal to the right hand limit.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    DBA
    DBA is offline
    Member
    Joined
    May 2009
    Posts
    129
    Thanks you for the answer. But my problem is it, to define the limit without a graph.
    With a graph I can see in which direction the infinity goes, but without that, how can I see if it is negative or positive infinity?

    Thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. infinite Limit
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 23rd 2010, 06:53 PM
  2. A Limit (Maybe using the infinite series?)
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 24th 2010, 05:15 AM
  3. Infinite Sum Limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 24th 2010, 05:53 PM
  4. Infinite Limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 24th 2008, 07:33 PM
  5. need help plz infinite limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 8th 2006, 08:06 AM

Search Tags


/mathhelpforum @mathhelpforum