limit x to inf of (1-(2/x))^(3x)

Question

anonymous · Answer

$$\LARGE \lim_{x\to \infty} \;\left(1-\frac2x\right)^{3x}$$  Do you mean this??

anonymous · Answer

yes thats what i mean, sorry for the way i typed it

anonymous · Answer

Never mind... ;)  

$$\LARGE \lim_{x\to \infty} \;\left(1-\frac{1}{\cfrac2x}\right)^{3x}= \lim_{x\to \infty} \;\left[\left(1-\frac{1}{\cfrac2x}\right)^{\frac2x\cdot \frac x2}\right]^{3x}$$

$$\Large \lim_{x\to \infty} \;\left[\left(1-\frac{1}{\cfrac2x}\right)^{\frac2x}\right]^{\frac{3x^2}{2}}$$

$$\Huge \lim_{x\to \infty}\;\; e^{\frac{3x^2}{2}}$$


can you continue ??

anonymous · Answer

ahhh.. I made a mistake at principal... it's not 1/(2x)  it is 1/(x/2)   just replace that.. and follow the steps !

anonymous · Answer

i cant sorry. you mind finishing it for me?

anonymous · Answer

It's hard with latex... it takes time.. I have to go to school, after 30 minutes ! ...

anonymous · Answer

ask your teacher, he'll guide you ! Have nice day !

anonymous · Answer

thanks

anonymous · Answer

Glad to help :)

anonymous · Answer

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