
MHB Master
#1
September 13th, 2019,
17:51
$\displaystyle\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)^{bx}$
Ok Im a little stumped already because we have 3 variables in this a,x and b
WA returned $e^{ab}$ but not what the steps are, maybe next....
$\displaystyle bx\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)$
Last edited by karush; September 13th, 2019 at 18:19.

September 13th, 2019 17:51
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MHB Craftsman
#2
September 13th, 2019,
18:18
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?

MHB Master
#3
September 13th, 2019,
18:23
Thread Author
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