Question

Evaluate.
\[\lim_{x \rightarrow -\infty} \ln ^{2x}\]

Answer 1

I don't understand why the answer is neg infinity

Answer 2

Or did I wrote it wrong, should it be this:
\[\lim_{x \rightarrow -\infty}\ln ^{2^{x}}\] ?
(This is my class notes, there's a possibility that I wrote the function wrong :/)

Answer 3

Ahh sorry :D ok game just ended.
So what .. what now?
Is the 2^x supposed to be inside the log?
doesn't really make sense otherwise.

Answer 4

Do you think it's this one?\[\Large\rm \lim_{x\to-\infty}\ln(2^x)\]or this one?\[\Large\rm \lim_{x\to-\infty}\ln^2(x)\]

Answer 5

or this? (ln x)^(2x)

bahh im confused +_+

Answer 6

I think is the first one or the third way... Sorry. My notes wasn't clear...

Answer 7

OK yah the first one makes sense with the answer you provided.

Answer 8

\[\Large\rm \lim_{x\to-\infty}\ln(2^x)\quad=\quad \ln\left(2^{(-\infty)}\right)\quad *\]So you can think of that 2 as becoming really really really small, because of the negative in the exponent, ya?
Remember how Rational was explaining that in a previous problem?

Answer 9

\[\Large\rm =\ln(0)\quad*\]

Answer 10

And you recall that the log function is asymptotic at x=0?

Answer 11

Going down down down, ya?