Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Need help Proving infinite limit properties.

  1. Sep 5, 2011 #1
    Suppose that limx->c f(x) = infinity and limx->c g(x)=l where l is a real number. Prove the following.
    limx->c[f(x)+g(x)]= infinity
    limx->c[f(x)g(x)]= infinity if l > 0
    limx->c[f(x)g(x)]= -infinity if l < 0

    I have the proof for these already, but I couldn't understand them, would someone please explain them.
    The thing I don't understand is where does the L come from, but explanation in general would be greatly appreciated

    Here is the proof for the second one:


    Uploaded with ImageShack.us[/PLAIN]
    Last edited: Sep 5, 2011
  2. jcsd
  3. Sep 5, 2011 #2


    User Avatar
    Science Advisor

    There seems to be a change of notation. In the original, g -> c when x -> a. In the equations in question, g -> L when x -> c.
  4. Sep 5, 2011 #3
    sorry, i corrected it, does anyone have the explanation for this proof ?
  5. Sep 5, 2011 #4
    What do you mean "where does the L come from"? It is the limit of the function g(x).

    I remind you, what you need to prove, is that given an M>0, you can find a [itex]\delta>0[/itex], so that for every x that satisfied |x-c|<[itex]\delta[/itex],
    |f(x)g(x)| > M hold.

    The proof shows the existence of such a [itex]\delta>0[/itex].

    In order to do this alone, however, you should start from the end. You should ask yourself, how can I make |f(x)g(x)| > M happen?
    You need to remember that f(x) can be as big as you want when you're close enough to c, and that g(x) can be as close to L as you'd like when you're close enough to c.

    That's exactly what they used in the proof.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook