What is the limit as x approaches 3 of (x^2)/(x!) ?

The limit as x approaches 3 of (x^2)/(x!) is 3/2

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limit as x approaches 3 of (x^2)/(x!)

x \to 3 lim (\frac{x ^{2}}{x !})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

x \to 3 lim (\frac{x ^{2}}{x !})

Plug in the value

x = 3

= \frac{3 ^{2}}{3 !}

Simplify

\frac{3 ^{2}}{3 !} : \frac{3}{2}

= \frac{3}{2}

x \to 3 lim (x^{3} e^{- x})

x \to 3 lim (ln (e^{x} + 1))

x \to 3 lim (\frac{3}{( x + 1 ) ^{2}})

x \to 3 lim ((\frac{2}{3})^{\frac{1}{x}})

x \to 3 lim (\frac{1}{ln ( x )})

What is the limit as x approaches 3 of (x^2)/(x!) ?
The limit as x approaches 3 of (x^2)/(x!) is 3/2