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Math Help - limit

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    limit

    Find \lim_{n\to \infty} \frac{n^5+2\sin n}{e^{-n}+6n^5}.
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  2. #2
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    Quote Originally Posted by peteryellow View Post
    Find \lim_{n\to \infty} \frac{n^5+2\sin n}{e^{-n}+6n^5}.
    the largest that 2\sin(n) can ever be is 2.

    e^{-n} \to 0 really fast as n \to \infty

    so, in essense you have a fraction on the order of \frac{n^5 + k}{6n^5} , where -2 \le k \le 2

    the limit is \frac{1}{6}
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