Question

limit. Exponential LHospital.
limit (1-2x)^(3/x) as x->0

Answer 1

\[\lim_{x \rightarrow 0} (1-2x)^{3/x}\]
I might be able to start using the fact \[(1+\frac{ 1 }{ x })^{x} = e\] but I'm not sure how to continue. or try with ln,
\[= \lim_{x \rightarrow 0} \frac{ 3 }{ x } \ln (1-\frac{ 1 }{ x })\]
\[= \lim_{x \rightarrow 0}\frac{ \ln(1-\frac{ 1 }{ x } )}{ \frac{ x }{ 3 } }\]
but I'm not sure how to continue from there either.

Answer 2

argh, I wish you could edit these replies. in the ln route, the 1/x should be 2x.