In order that the function f(x) = (x + 1)cotx is continuous at x = 0,…

$\underset{x→0}{\lim}f(x)=\underset{x→0}{\lim}(x+1)^{\cot x}$ (1^∞ form)

or $\underset{x→0}{\lim}=\underset{x→0}{\lim}[(1+x)^{1/x}]^{\frac{x}{\tan x}}=e^1$ ⇒ f(0) = e.

Hence (B) is the correct answer.