Given $f(x)=\frac{3^{3x}-1}{12x}$:

$($a$)$ Use a for loop $($list comprehension$)$ to evaluate the function at $x=-0\mathrm{.}1,-0\mathrm{.}01,-0\mathrm{.}001,-0\mathrm{.}0001,$ then at $x=0\mathrm{.}1,0\mathrm{.}01,0\mathrm{.}001,0\mathrm{.}0001$ to numerically estimate $\underset{x0}{lim}f(x).$

$($b$)$ Plot $f$ on the interval $-1,1$ to graphically verify your estimate in part $($a$).$

$($c$)$ Directly compute $\underset{x0}{lim}f(x)$ and convert it to a decimal approximation to compare with your estimate in part $($a$).$