Question

How do I find the limx->0 of ln((1+x)^(5/x)). I think it has something to do with L'Hop's rule but I can't see how it is 0/0 of infinity/infinity. Thanks :)

Answer 1

Bring the 5/x down

Answer 2

\[\lim_{x \rightarrow 0} \frac{5 \ln(1+x)}{x}\]

Answer 3

you have 0/0

Answer 4

for some reason the equation is just coming up as characters on my computer...can you write it out using the draw tool for me please :)

Answer 5

refresh your browser

Answer 6

thanks :)

Answer 7

any idea what
\[\lim_{x\to 0}(1+x)^{\frac{5}{x}}\] is?

Answer 8

well I would have made it \[x \sqrt{(1+x)^{5}} \] and so them the lim x-> 0 would be 0. Right?

Answer 9

no

Answer 10

oh...um...help?! :)

Answer 11

take urp @freckles suggestion

Answer 12

But I don't understand how they bought it down. What rule is that?

Answer 13

power rule for log

Answer 14

\[\ln(x^r)=r \ln(x)\]

Answer 15

oh...oops...forgot about that one :)
so if we did that...
\[\frac{ 5*\ln(1+0) }{ 0 }\]
\[\frac{ 0 }{ 0}\]

Answer 16

because ln(1) = 0 yes?

Answer 17

yes ln(1) is 0