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Limit of the function cos(x)/factorial(x)

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     /cos(x)\
 lim |------|
x->oo\  x!  /

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

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

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

Rapid solution [src]

0

Expand and simplify

Other limits x→0, -oo, +oo, 1

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

\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{x!}\right) = 1

\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x!}\right) = 1

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

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

\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x!}\right) = \frac{\left\langle -1, 1\right\rangle}{\left(-\infty\right)!}