Find the $\displaystyle \lim_{x \to \infty} e^{x^2}$

$ \begin{equation} \begin{aligned} \lim_{x \to \infty} e^{-x^2} =& \lim_{x \to \infty} \frac{1}{e^{x^2}} \\ \\ =& \frac{1}{e^{\infty^2}} \\ \\ =& \frac{1}{e^{\infty}} \\ \\ =& \frac{1}{\infty} \\ \\ =& 0 \end{aligned} \end{equation} $

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