Question

$\underset{x\to 0}{\lim }\frac{x}{\tan x}\mathrm{is}$

(a) 0
(b) 1
(c) 4
(d) not defined

Answer 1

(b) 1

$$\begin{gathered} \underset{x\to 0}{\lim }\frac{x}{\tan x} \\ =\underset{x\to 0}{\lim }\frac{1}{{\displaystyle \frac{\tan x}{x}}} \\ =\frac{1}{1} \\ =1 \end{gathered}$$