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

The limit as x approaches e of x^2*e^{x^2} is e^{2+e^2}

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limit as x approaches e of x^2*e^{x^2}

x \to e lim (x^{2} \cdot e^{x^{2}})

e^{2 + e^{2}}

Decimal

11956.80796 \dots

Solution steps

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

Plug in the value

x = e

= e^{2} e^{e^{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{2} e^{e^{2}} = e^{2 + e^{2}}

= e^{2 + e^{2}}

What is the limit as x approaches e of x^2*e^{x^2} ?
The limit as x approaches e of x^2*e^{x^2} is e^{2+e^2}