# Thread: lim (1-(3/x))^x

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

lim (1-(3/x))^x
x to +infinity

2. Originally Posted by maiya

lim (1-(3/x))^x
x to +infinity
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:

$\displaystyle \lim_{n \to +\infty}\left(1-\frac1n \right)^{3n} =\left( \lim_{n \to +\infty}\left(1-\frac1n \right)^{n}\right)^3 = e^3$

3. Originally Posted by earboth
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:

$\displaystyle \lim_{n \to +\infty}\left(1-\frac1n \right)^{3n} =\left( \lim_{n \to +\infty}\left(1-\frac1n \right)^{n}\right)^3 = e^3$
tqvm..

4. Originally Posted by Random Variable
tqvm..