Limits help

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Nov 11th 2008, 04:15 AM
thelostchild

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 :)
Nov 11th 2008, 04:22 AM
mr fantastic

Quote:

Originally Posted by thelostchild

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 :)

$\frac{5^{n+2}-7^{n+2}}{5^n-7^n} = \frac{5^2 \cdot 5^{n} - 7^2 \cdot 7^{n}}{5^n-7^n} = \frac{5^2 \cdot \left(\frac{5}{7}\right)^{n} - 7^2}{\left(\frac{5}{7}\right)^n - 1} \rightarrow \frac{0 - 49}{0 - 1} = 49$ .
Nov 11th 2008, 04:25 AM
thelostchild

Quote:

Originally Posted by mr fantastic

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

thank you, I really just needed to be shown one like this makes me feel stupid now though!
Nov 11th 2008, 04:29 AM
mr fantastic

Quote:

Originally Posted by thelostchild

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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