Q. If $f(x) = (x + 1)^{\cot x}$ be continuous at $= 0$, then $f(0)$ is equal to
A) 0
B) $- e$
C) $e$
D) None of these
Explanation
(c)
$\lim_{x \rightarrow 0}(1 + x)^{\cot{\ x}} = \lim_{x \rightarrow 0}\ \left\{ (1 + x)^{\frac{1}{x}} \right\}^{x\cot x}$
$= \lim_{x \rightarrow 0}\ \ \ e^{x\cot x} = e$
Since $f(x)$ is continuous at $x = 0$
$\therefore\ \ \ \ \ f(0) = \ \lim_{x \rightarrow 0}\ f(x) = e$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.