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Math Help - Limits help

  1. #1
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    Limits help

    Hi

    feeling very stupid here any chance of a push in the right direction with this

     \lim_{x \rightarrow \infty} \frac{5^{n+2}-7^{n+2}}{5^n-7^n}

    any hints would be appreciated

    Cheers

    Simon
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  2. #2
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    Quote Originally Posted by thelostchild View Post
    Hi

    feeling very stupid here any chance of a push in the right direction with this

     \lim_{x \rightarrow \infty} \frac{5^{n+2}-7^{n+2}}{5^n-7^n}

    any hints would be appreciated

    Cheers

    Simon
    \frac{5^{n+2}-7^{n+2}}{5^n-7^n} = \frac{5^2 \cdot 5^{n} - 7^2 \cdot 7^{n}}{5^n-7^n} = \frac{5^2 \cdot \left(\frac{5}{7}\right)^{n} - 7^2}{\left(\frac{5}{7}\right)^n - 1} \rightarrow \frac{0 - 49}{0 - 1} = 49.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    \frac{5^{n+2}-7^{n+2}}{5^n-7^n} = \frac{5^2 \cdot 5^{n} - 7^2 \cdot 7^{n}}{5^n-7^n} = \frac{5^2 \cdot \left(\frac{5}{7}\right)^{n} - 7^2}{\left(\frac{5}{7}\right)^n - 1} \rightarrow \frac{0 - 49}{0 - 1} = 49.
    thank you, I really just needed to be shown one like this makes me feel stupid now though!
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  4. #4
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    Quote Originally Posted by thelostchild View Post
    thank you, I really just needed to be shown one like this makes me feel stupid now though!
    Better to feel stupid now than in the exam.
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