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I'm wrong, but I can't figure out how.

  1. May 9, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\lim_{x\rightarrow\infty} \sqrt{e^{2x}+9}-e^x[/tex]

    2. Relevant equations
    [tex]\lim_{x\rightarrow\infty} \sqrt{x} = \infty[/tex]
    [tex]\lim_{x\rightarrow\infty} e^x = \infty [/tex]

    3. The attempt at a solution

    [tex]\lim_{x\rightarrow\infty} \sqrt{e^{2x}+9}-e^x = \lim_{x\rightarrow\infty} \frac{e^{2x}+9-e^{2x}}{\sqrt{e^{2x}+9}+e^x}[/tex]
    [tex]=\lim_{x\rightarrow\infty} \frac{9}{\sqrt{e^{2x}+9}+e^x}[/tex]

    The limit as x>infty of sqrt(x) is infty
    the limit as x>infty of e^2x is infty
    the entire bottom term tends towards infinity as x tends towards infinity
    [tex]\lim_{x\rightarrow\infty} \frac{9}{\sqrt{e^{2x}+9}+e^x}=0[/tex]

    My professor had a different answer that we didn't have time to go over in class, and my answer just doesn't feel right. Where did I make my mistake?
  2. jcsd
  3. May 9, 2009 #2


    Staff: Mentor

    Looks fine to me. I don't see how your professor could come up with a different value unless the two of you started from different problems.
  4. May 9, 2009 #3
    Thanks, I've been running through this again and again for the past couple days.
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