What is the limit as x approaches 3 of x^3e^{-x} ?

The limit as x approaches 3 of x^3e^{-x} is (27)/(e^3)

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limit as x approaches 3 of x^3e^{-x}

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

\frac{27}{e ^{3}}

Decimal Notation

1.34425 \dots

Solution steps

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

Plug in the value

x = 3

= 3^{3} e^{- 3}

Simplify

3^{3} e^{- 3} : \frac{27}{e ^{3}}

= \frac{27}{e ^{3}}

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 )})

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

What is the limit as x approaches 3 of x^3e^{-x} ?
The limit as x approaches 3 of x^3e^{-x} is (27)/(e^3)