horizontal asymptotes

[smita411]

i know there are some identities when it comes to horizontal asymptotes
when it is
lim (1/4)^x
x-->infinity
is there an identity for that one?
also while doing the limits to infinity if you have
5^x is this the same as e^x ?

thanks

 

[skeeter]

$\displaystyle \left(\frac{1}{4}\right)^x = \frac{1^x}{4^x} = \frac{1}{4^x}$

now, what happens to the value of $\displaystyle \frac{1}{4^x}$ as $\displaystyle x\to\infty$ ?