$(5$ pts$)$ Task $7$: Write down the Taylor series expansion of the function

$\backslash [$

$\backslash$boldsymbol$\{$f$\}(\backslash$boldsymbol$\{$x$\})=\backslash$boldsymbol$\{$e$\}^\{$x$^\{2\}\}$

$\backslash ]$

at a single point $\backslash ($ c$=1\backslash ),$ where $\backslash ($ x $\backslash )$ is a scalar variable. The expansion should be presented with at least the first $3$ terms. Please provide detailed steps on how to get the answer.