If the following function $f(x)$ is continuous at $x = 0$, then write the value of $k$. $f(x) = \begin{cases} \frac{\sin \frac{3x}{2}}{x}, & x \neq 0 \\ k, & x = 0 \end{cases}$

$k = \frac{3}{2}$

The correct answer is Option (2) → $k = \frac{3}{2}$ ##

$\lim\limits_{x \to 0} \frac{\sin \frac{3x}{2}}{x} = \lim\limits_{x \to 0} \frac{3}{2} \cdot \frac{\sin \frac{3x}{2}}{\frac{3x}{2}}$

or $k = \frac{3}{2}$