The given reaction is an example of the Hell-Volhard-Zelinsky (HVZ) reaction, which selectively brominates the $\alpha$-carbon of carboxylic acids in the presence of Br$_2$ and red phosphorus. The reaction mechanism involves the formation of an $\alpha$-brominated carboxylic acid.
\[\text{COOH} \xrightarrow{\text{Br}_2/\text{Red P}} \text{COOH-Br} \xrightarrow{\text{H}_2\text{O}} \text{COOH-Br (Product)}\]
Thus, the product formed is the $\alpha$-bromo derivative of the given carboxylic acid.
Let $ f(x) = \begin{cases} (1+ax)^{1/x} & , x<0 \\1+b & , x = 0 \\\frac{(x+4)^{1/2} - 2}{(x+c)^{1/3} - 2} & , x>0 \end{cases} $ be continuous at x = 0. Then $ e^a bc $ is equal to
Total number of nucleophiles from the following is: \(\text{NH}_3, PhSH, (H_3C_2S)_2, H_2C = CH_2, OH−, H_3O+, (CH_3)_2CO, NCH_3\)