Limits help

Hi

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

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

any hints would be appreciated

Cheers

Simon :)

Quote:

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Originally Posted by thelostchild

Hi

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

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

any hints would be appreciated

Cheers

Simon :)

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$\displaystyle \frac{5^{n+2}-7^{n+2}}{5^n-7^n} = \frac{5^2 \cdot 5^{n} - 7^2 \cdot 7^{n}}{5^n-7^n} = \frac{5^2 \cdot \left(\frac{5}{7}\right)^{n} - 7^2}{\left(\frac{5}{7}\right)^n - 1} \rightarrow \frac{0 - 49}{0 - 1} = 49$.

Quote:

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Originally Posted by mr fantastic

$\displaystyle \frac{5^{n+2}-7^{n+2}}{5^n-7^n} = \frac{5^2 \cdot 5^{n} - 7^2 \cdot 7^{n}}{5^n-7^n} = \frac{5^2 \cdot \left(\frac{5}{7}\right)^{n} - 7^2}{\left(\frac{5}{7}\right)^n - 1} \rightarrow \frac{0 - 49}{0 - 1} = 49$.

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thank you, I really just needed to be shown one like this makes me feel stupid now though!

Quote:

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Originally Posted by thelostchild

thank you, I really just needed to be shown one like this makes me feel stupid now though!

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Better to feel stupid now than in the exam.