Question

Use l'Hopital's rule to find \[\lim_{x \rightarrow \infty}(1+\frac{ 2 }{ x ^{3} })^{x}\]

Answer 1

taking log of the function inside the limit you get
\[\frac{ \ln (1+\frac{ 2 }{ x ^{3} }) }{ \frac{ 1 }{ x } }\]

Answer 2

which is 0/0 form so now you can use l hopital

Answer 3

once you get the answer take the log of it to get the actual answer