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Math Help - Limit problems with e and ln

  1. #1
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    Limit problems with e and ln

    \lim_{x \to +\infty} \frac {x^4}{e^x}

    \lim_{x \to +\infty} \frac {\ln x}{x}

    Can anyone show me how these limit reaches to 0?
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  2. #2
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    Quote Originally Posted by chengbin View Post
    \lim_{x \to +\infty} \frac {x^4}{e^x}

    \lim_{x \to +\infty} \frac {\ln x}{x}

    Can anyone show me how these limit reaches to 0?
    Use l'Hospital's rule 4 times for the first limit and once for the second.
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  3. #3
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    Quote Originally Posted by chengbin View Post
    \lim_{x \to +\infty} \frac {x^4}{e^x}

    \lim_{x \to +\infty} \frac {\ln x}{x}

    Can anyone show me how these limit reaches to 0?
    \lim_{x \to +\infty} \frac {x^4}{e^x} = 0 = \lim_{x \to +\infty} \frac {\ln x}{x}, because you know that

    x^4 < e^x \ \& \ ln x < x for big x

    Proof by using L'Hospital
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