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Math Help - Is this true?

  1. #1
    Junior Member
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    Is this true?

    \lim_{x\rightarrow\infty}f(x) = e^{\lim_{x\rightarrow\infty}ln(f(x))}


    I think I've seen or used this before but it might've just been something similar, I don't have my calculus book handy.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by HD09 View Post
    \lim_{x\rightarrow\infty}f(x) = e^{\lim_{x\rightarrow\infty}ln(f(x))}


    I think I've seen or used this before but it might've just been something similar, I don't have my calculus book handy.
    If the limit exists, yes. The quick way using only continuity is that \lim_{x\to\infty}f(x)=\lim_{z\to 0}f\left(\frac{1}{z}\right)=\lim_{z\to 0}\text{exp}\left(\ln\left(f\left(\frac{1}{z}\righ  t)\right)\right)=\text{exp}\left(\lim_{z\to 0}\ln\left(f\left(\frac{1}{z}\right)\right)\right) and work backwards.
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