What is the limit as x approaches 1 of x^4e^{-x^2} ?

The limit as x approaches 1 of x^4e^{-x^2} is 1/e

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limit as x approaches 1 of x^4e^{-x^2}

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

\frac{1}{e}

Decimal

0.36787 \dots

Solution steps

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

Plug in the value

x = 1

= 1^{4} e^{- 1^{2}}

Simplify

1^{4} e^{- 1^{2}} : \frac{1}{e}

= \frac{1}{e}

What is the limit as x approaches 1 of x^4e^{-x^2} ?
The limit as x approaches 1 of x^4e^{-x^2} is 1/e