Given $f(x)=e^{\frac{-x^2}{2}},($note that the entire fraction is in the exponent$)$

$($a$)$ Find the equation of the line tangent to $f$ at $x=1.$

$($b$)$ Find the equation of the normal line of $f$ at $x=1.$

$($c$)$ Plot $f,$ along with both lines you found, on the same set of axes over $x-$interval $0,3$ wit $y-$interval $0,3.$

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