What is the limit as x approaches infinity of 3/(x!) ?

The limit as x approaches infinity of 3/(x!) is 0

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limit as x approaches infinity of 3/(x!)

x \to \infty lim (\frac{3}{x !})

0

Solution steps

x \to \infty lim (\frac{3}{x !})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to \infty lim (\frac{1}{x !})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 3 \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( x ! )}

x \to \infty lim (1) = 1

x \to \infty lim (x!) = \infty

= 3 \cdot \frac{1}{\infty}

Simplify

3 \cdot \frac{1}{\infty} : 0

= 0

x \to 0 + lim (2 x^{2} - x)

x \to 1 + lim (\frac{- 5}{1 - x})

x \to \frac{π}{4} lim (sec (2 x))

\frac{1}{( \frac{1}{x} )} \to (\frac{1}{x}) lim (\frac{1}{( \frac{1}{x} )})

x \to 0 lim (+ (x^{2}))

What is the limit as x approaches infinity of 3/(x!) ?
The limit as x approaches infinity of 3/(x!) is 0