# Thread: 6.6.60 limiit possible L'H

1. $\displaystyle\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)^{bx}$

Ok Im a little stumped already because we have 3 variables in this a,x and b

W|A returned $e^{ab}$ but not what the steps are, maybe next....

$\displaystyle bx\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)$

2.

3. Originally Posted by karush
$\displaystyle\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)^{bx}$

Ok Im a little stumped already because we have 3 variables in this a,x and b
note that $a$ and $b$ represent constants, and ...

$\displaystyle\lim_{{x}\to{\infty}}\left(1+\dfrac{1}{x}\right)^x = e$

$\displaystyle\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)^x = e^a$

... so, what happens to the limit with the constant "$b$" thrown in as an outer exponent?

not sure if this is the correct way to say it
but are they not just scalars

concering what is inside the () can that be distributed or added together