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

**maiya** · May 25th 2010, 12:33 AM

Please help me how to resolve this calculus...

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

**earboth** · May 25th 2010, 12:38 AM

Originally Posted by maiya

Please help me how to resolve this calculus...

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

1. You are supposed to know that $\lim_{n \to +\infty}\left(1 - \frac1n\right)^n = e$

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

3. Your limit becomes now:

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

**Random Variable** · May 25th 2010, 12:45 AM

http://www.mathhelpforum.com/math-he...183-post3.html

**maiya** · May 25th 2010, 08:41 AM

Originally Posted by earboth

1. You are supposed to know that $\lim_{n \to +\infty}\left(1 - \frac1n\right)^n = e$

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

3. Your limit becomes now:

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

tqvm..

**maiya** · May 25th 2010, 08:43 AM

Originally Posted by Random Variable

http://www.mathhelpforum.com/math-he...183-post3.html

tqvm..

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