Let \(f\left(\mathrm{x}\right)=\left{\begin{matrix}(1+\mathrm{ax}{)}^{1/\mathrm{x}} & , & \mathrm{x} 0\end{matrix}\right…

Let \(f\left(\mathrm{x}\right)=\left{\begin{matrix}(1+\mathrm{ax}{)}^{1/\mathrm{x}} & , & \mathrm{x}<0 \\ 1+\mathrm{b} & , & \mathrm{x}=0 \\ \frac{(\mathrm{x}+4{)}^{1/2}-2}{(\mathrm{x}+\mathrm{c}{)}^{1/3}-2} & , & \mathrm{x}>0\end{matrix}\right.\)

be continuous at \(\mathrm{x}=0\). Then \({\mathrm{e}}^{\mathrm{a}}\mathrm{bc}\) is equal to

[JEE Main 2025, 3 Apr (Shift 1)]