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Math Help - limits at infinity of natural logs

  1. #1
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    limits at infinity of natural logs

    I have to do this for tomorrow and I have no clue how to solve this problem:

    For what functions f(x) and g(x) below, will the \lim_{x\rightarrow \infty} \frac{f(x)}{g(x)}=0?

    a) f(x)=e^x, g(x) = x^2
    b) f(x)=e^x, g(x)=ln (x)
    c) f(x)=ln (x), g(x)=e^x
    d) f(x)=x, g(x)=ln (x)
    e) f(x)=3^x, g(x)=2^x

    Thanks
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  2. #2
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    Try using dHopital's rule on each of the answer and see what happens.
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  3. #3
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    I've never entirely understood l'Hopital's rule so I'm not sure how to apply it in this case.
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  4. #4
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    In limit equations, if the numerator AND the denominator may be defined as one of the following due to the limit - zero, negative infinity, or positive infinity - then you repeatedly take the derivative of the numerator and denominator (DON'T USE THE QUOTIENT RULE, JUST TAKE EACH SEPARATE DERIVATIVE) until either the numerator or the denominator cannot be defined as zero, negative infinity, or positive infinity. When that happens, just plug in the limit and you got your number. With some practice, it's very, very effective. Do yourself a favor and learn it well, it'll pay off. It's very important.
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