Option : (C)
Formula : -
(i) \(\lim\limits_{x \to 0}\frac{log(1-x)}{x}\) = 1 and \(\lim\limits_{x \to 0}\frac{sin\,x}{x}\) = 1
(ii) A function f(x) is said to be continuous at a point x=a of its domain, if \(\lim\limits_{x \to a}f(x)\) = f(a)
\(\lim\limits_{x \to a^+}f(a+h)\) = \(\lim\limits_{x \to a^-}f(a-h)\) = f(a)
(iii) \(\lim\limits_{x \to a}{\{f(x).g(x)}\}\) = 1.m,
Where \(\lim\limits_{x \to a}f(x)\) = 1, \(\lim\limits_{x \to a}g(x)\) = m
Given :-
f(x) = (x + 1) cotx
log f(x)=(cotx)(log(x+1)) ….taking log both sides
f(0) = e
