What is the limit as x approaches 0 of x^3e^{-3x} ?

The limit as x approaches 0 of x^3e^{-3x} is 0

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limit as x approaches 0 of x^3e^{-3x}

x \to 0 lim (x^{3} e^{- 3 x})

0

Solution steps

x \to 0 lim (x^{3} e^{- 3 x})

Plug in the value

x = 0

= 0^{3} e^{- 3 \cdot 0}

Simplify

= 0

x \to 0 lim (x (csc (4 x)))

x \to 0 lim (sin^{3} (x))

x \to \infty lim (\frac{cosh ( x )}{e ^{x}})

x \to 0 lim (sin^{2} (\frac{1}{x}))

x \to - 1 lim (3 x^{3} - 4 x^{2} - 3)

What is the limit as x approaches 0 of x^3e^{-3x} ?
The limit as x approaches 0 of x^3e^{-3x} is 0