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

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

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

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

\frac{1}{e}

Decimal

0.36787 \dots

Solution steps

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

Plug in the value

x = 1

= e^{- 1^{2}}

Simplify

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

= \frac{1}{e}

x \to 1 + lim (- x)

x \to \frac{π}{2} lim (\frac{cos ^{2} ( x )}{( sin ( \frac{1}{2} ) x - cos ( \frac{1}{2} ) x ) ^{2}})

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

x \to 0 lim (9 - x^{2})

x \to \infty lim (\frac{3 x ^{6} + 3 x ^{2} + 2}{7 x ^{6} + x - 1})

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