Please help me how to resolve this calculus...

lim (1-(3/x))^x

x to +infinity

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- May 25th 2010, 12:33 AMmaiyalim (1-(3/x))^x
Please help me how to resolve this calculus...

lim (1-(3/x))^x

x to +infinity - May 25th 2010, 12:38 AMearboth
1. You are supposed to know that $\displaystyle \lim_{n \to +\infty}\left(1 - \frac1n\right)^n = e$

2. Use the substitution $\displaystyle \frac3x =\frac1n~\implies~x=3n$

3. Your limit becomes now:

$\displaystyle \lim_{n \to +\infty}\left(1-\frac1n \right)^{3n} =\left( \lim_{n \to +\infty}\left(1-\frac1n \right)^{n}\right)^3 = e^3$ - May 25th 2010, 12:45 AMRandom Variable
- May 25th 2010, 08:41 AMmaiya
- May 25th 2010, 08:43 AMmaiya