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

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

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limit as x approaches 0 of xe^{-x}

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

0

Solution steps

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

Plug in the value

x = 0

= 0 \cdot e^{- 0}

Simplify

= 0

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