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Math Help - limit

  1. #1
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    limit

    Show your work and calculate limit of the following questions.



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  2. #2
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    For the first problem, which do you mean?
     \lim_{x \to \infty} 3 \sqrt{n}^\frac {1} {2n}
    or
     \lim_{x \to \infty} 3 \sqrt{n}^{\frac {1} {2} n}

    2nd problem

     \lim_{x \to \infty} (n+1)^\frac {1} {ln(n+1)}
    Take the ln of the lim, just remember to rise it to e later.
     \lim_{x \to \infty} \frac {ln(n+1)} {ln(n+1)}





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  3. #3
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    the first way you wrote it. and how can i just take the ln and do what you said for the second problem
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  4. #4
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    I took the ln for you in problem 2...I guess i'll show it to you step by step

     \lim_{x \to \infty} (n+1)^\frac {1} {ln(n+1)}
    Just remember to rise the answer to e.
     \lim_{x \to \infty} ln(n+1)^\frac {1} {ln(n+1)}
    By the law of lns..
     \lim_{x \to \infty} \frac {1} {ln(n+1)}ln(n+1)
    <br /> <br />
\lim_{x \to \infty} \frac {ln(n+1)} {ln(n+1)}=1<br />
    So the answer will be  e^1 or just plain e.

    Try the first problem this way. You will probably need to l'hospital it.
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  5. #5
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    Quote Originally Posted by Linnus View Post
    I took the ln for you in problem 2...I guess i'll show it to you step by step

     \lim_{x \to \infty} (n+1)^\frac {1} {ln(n+1)}
    Just remember to rise the answer to e.
     \lim_{x \to \infty} ln(n+1)^\frac {1} {ln(n+1)}
    By the law of lns..
     \lim_{x \to \infty} \frac {1} {ln(n+1)}ln(n+1)
    <br /> <br />
\lim_{x \to \infty} \frac {ln(n+1)} {ln(n+1)}=1<br />
    So the answer will be  e^1 or just plain e.

    Try the first problem this way. You will probably need to l'hospital it.
    cant use lhospital rule, so i dont know how to do it. Thats the problem i am having
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  6. #6
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    Have you tried it? I just did and you don't actually need l'hospital.

    <br /> <br />
\lim_{n \to \infty} 3 \sqrt{n}^\frac {1} {2n}<br />

    <br />
3 \lim_{n \to \infty}  \sqrt{n}^\frac {1} {2n}<br />

    <br />
3 \lim_{n \to \infty} \frac {ln\sqrt {n}} {2n}<br />

    It should be obvious from here. Remeber just rise the limit to e, not including the 3.

    <br />
3 \lim_{n \to \infty} \frac {\ln {n}} {4n}<br />


    Last edited by Linnus; September 25th 2008 at 04:45 PM.
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  7. #7
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    Quote Originally Posted by Linnus View Post
    Have you tried it? I just did and you don't actually need l'hospital.

    <br /> <br />
\lim_{x \to \infty} 3 \sqrt{n}^\frac {1} {2n}<br />

    <br />
3 \lim_{x \to \infty}  \sqrt{n}^\frac {1} {2n}<br />

    <br />
3 \lim_{x \to \infty} \frac {ln\sqrt {n}} {2n}<br />

    It should be obvious from here. Remeber just rise the limit to e, not including the 3.

    <br />
3 \lim_{x \to \infty} \frac {\ln {n}} {4n}<br />


    I figuered it out. Its really quite simple. Just take the take the limit of the product so we have limit of 3^1/2n *limit of ((n)^(1/2))^(1/2n)

    the limit of the first part is 1 since 1/2n will approch o and 3^0 is 1 and then same thing for the second part so 1*1 is 1
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