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  1. MHB Master
    \(\displaystyle \int\)
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    #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....

    $\displaystyle bx\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)$
    Last edited by karush; September 13th, 2019 at 18:19.

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    #2
    Quote Originally Posted by karush View Post
    $\displaystyle\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)^{bx}$

    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?

  4. MHB Master
    \(\displaystyle \int\)
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    #3 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

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