$$\lim_{x \to \infty}\left(2^{- x} x!\right) = \infty$$ $$\lim_{x \to 0^-}\left(2^{- x} x!\right) = 1$$ More at x→0 from the left $$\lim_{x \to 0^+}\left(2^{- x} x!\right) = 1$$ More at x→0 from the right $$\lim_{x \to 1^-}\left(2^{- x} x!\right) = \frac{1}{2}$$ More at x→1 from the left $$\lim_{x \to 1^+}\left(2^{- x} x!\right) = \frac{1}{2}$$ More at x→1 from the right $$\lim_{x \to -\infty}\left(2^{- x} x!\right) = \infty \left(-\infty\right)!$$ More at x→-oo