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Question related to inequalities and limits that go to infinity

  1. Feb 24, 2013 #1
    I want to show that if [itex] f(x) > g(x) [/itex] [itex] \forall x \in (-\infty, \infty) [/itex] and [itex] \displaystyle\lim_{x\to\infty}g(x)=\infty [/itex], then [itex] \displaystyle \lim_{x\to\infty}f(x)=\infty [/itex]. This result is true, correct? If so, what theorem should I use or reference to show this result? I wasn't sure if the squeeze theorem was application to this problem.
     
  2. jcsd
  3. Feb 24, 2013 #2
    Have you considered the Squeeze Theorem?
     
  4. Feb 24, 2013 #3
    I may be entirely incorrect, but I don't think the squeeze theorem would be very helpful. f(x) isn't "squeezed" between two functions.
     
  5. Feb 24, 2013 #4

    jbunniii

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    Consider what it means for ##\lim_{x \rightarrow \infty} g(x) = \infty## to be true. Given any ##Y \in \mathbb{R}##, there is some ##X \in \mathbb{R}## such that ##g(x) > Y## for all ##x > X##. Now apply the fact that ##f(x) > g(x)##.
     
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