Question

Can you apply L'Hopital's Rule multiple times? Also, help with finding the limit of (3x)^(1/3x) algebraically please?

Answer 1

as long as it's still \(\dfrac00\) or \(\dfrac\infty\infty\) you can use l'hopital rule as many times as you want

Answer 2

and what does x tend to?

Answer 3

Towards infinity again

Answer 4

you mean \(\Large\lim\limits_{x\rightarrow\infty}(3x)^{\frac13x}\)?

Answer 5

or \(\Large\lim\limits_{x\rightarrow\infty}(3x)^{\frac1{3x}}\)?

Answer 6

The second one, sorry for not clearing that up earlier

Answer 7

not your fault :)

Answer 8

try taking the log of that function :)

Answer 9

remember \(\large x=e^{\ln x}\)

Answer 10

I'm not quite sure how to do that

Answer 11

ok i'll do the first step for you :)

Answer 12

\[\Large\begin{array}{l}&\lim_{x\rightarrow\infty}(3x)^{\frac1{3x}}\\=&e^{\lim\limits_{x\rightarrow\infty}\ln(3x)^{\frac1{3x}}}\\=&e^{\lim\limits_{x\rightarrow\infty}\frac1{3x}\ln(3x)}\end{array}\]

Answer 13

now you can apply the l'hopital rule :)

Answer 14

How would I apply it in this case?