Question

evaluate the limit as x approaches infinity (1-(3/x))^(4x)

Answer 1

\[e^{-12}\] from your eyeballs

Answer 2

\[\lim_{x\rightarrow \infty}(1+\frac{1}{x})^x=e\] pretty much by definition, so
\[\lim_{x\rightarrow \infty}(1+\frac{-3}{x})^{4x}=e^{-12}\]