Show that `f(x)={((sin3x)/(tan2x) ,, if x<0),(3/2 ,, if x=0),((log(1+3x))/(e^(2x)-1) ,, ifx >0):} \ is \ c o n t i n u o u s \ a t \ x=0`

Explanation

To show that the function

\[
f(x) =
\begin{cases}
\frac{\sin(3x)}{\tan(2x)} & \text{if } x < 0 \\
\frac{3}{2} & \text{if } x = 0 \\
\frac{\log(1 + 3x)}{e^{2x} - 1} & \text{if } x > 0
...