engineering recuitment AAI ATC Junior Executive 2025 Mock Test Series Mathematics Limit and Continuity Continuity of a function
If \(\rm f(x)=\left\{\begin{matrix}\rm \dfrac{\sin 3x}{e^{2x}-1}, &\rm x \ne 0\\\rm k-2, &\rm x=0 \end{matrix}\right.\) is continuous at x = 0, then k = ?
1
\(\dfrac{3}{2}\)
2
\(\dfrac{9}{5}\)
3
\(\dfrac{1}{2}\)
4
\(\dfrac{7}{2}\)