# 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....

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

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?  Reply With Quote

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  Reply With Quote

+ Reply to Thread #### Tags for this Thread

6.6.60, limiit, stumped, variables #### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
• 