Limit of the function factorial(x)/x

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     /x!\
 lim |--|
x->oo\x /

\lim_{x \to \infty}\left(\frac{x!}{x}\right)

Limit(factorial(x)/x, x, oo, dir='-')

Rapid solution [src]

oo

\infty

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty}\left(\frac{x!}{x}\right) = \infty

\lim_{x \to 0^-}\left(\frac{x!}{x}\right) = -\infty

\lim_{x \to 0^+}\left(\frac{x!}{x}\right) = \infty

\lim_{x \to 1^-}\left(\frac{x!}{x}\right) = 1

\lim_{x \to 1^+}\left(\frac{x!}{x}\right) = 1

\lim_{x \to -\infty}\left(\frac{x!}{x}\right) = 0